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Old 9th-April-2013, 07:14 AM   #1
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Default The Limits of Infinity (Irony Recognized)

A quick question to throw out, hopefully to spark some interesting debate.

As a side note I'll accept my position as unofficial philosopher of the forum after stumbling upon a strikingly similar thought process between Thomas Nagel and I. I've actually used this exact comparison when attempting to explain subjectivity and consciousness without knowing he wrote a paper on it years ago. Strange. I digress:

To the question!

What exactly does infinity mean? Can it actually mean nothing? Can infinity be zero? The only way I can comprehend infinity is if it implies there is an unlimited amount of possibilities, which means there is no definite answer. We cannot know anything with absolute certainty, and infinity expresses this beautifully; so much so, that it implies nothing is actually happening.

You can't place a point on a number line to infinity. Therefore, there is no point.

If time is infinite, then there is no point in time to which we can point. Therefore, there is no time.

If the universe is infinite, then there is no point in the universe to which we can point. Therefore, there is no universe.


http://astrosociety.org/pubs/mercury/31_02/nothing.html

And:

Thoughts?
(What does this mean? Nothing )
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Old 9th-April-2013, 07:18 AM   #2
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Default Re: The Limits of Infinity (Irony Recognized)

[MENTION=2624]BigApplePi[/MENTION]
Simply because your avatar is infinity and I feel like you may give me some insight here.
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Old 9th-April-2013, 11:30 AM   #3
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Default Re: The Limits of Infinity (Irony Recognized)

Michio Kaku bugs me for some reason. Mainly because he's knowledgable, but not necessarily right. I differ with him on many points, but his reasonableness is deceptive.

At any rate I'd like to note that while infinity is definitely real in the mathematical sense, I'm not aware of any sightings in reality. Time isn't infinite, or at least doesn't have to be, the universe can end along with Time in a variety of ways. And regardless time appears to have had a beginning so it doesn't go infinitely backwards.

Space isn't infinite, since the Big Bang it's been getting bigger but has an enumerable size.

Division isn't infinite either, it appears that once you get down to the Planck length you find discreetness to the universe.

If I were to place a bet I'd put it on "doesn't exist".
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Old 9th-April-2013, 03:09 PM   #4
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Default Re: The Limits of Infinity (Irony Recognized)

Everyone and their mom seems to consider space infinite. Surely they must've missed Einstein and gotten stuck on Newtons idea of space in their vain attempts to quantify nothingness.
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Old 9th-April-2013, 03:27 PM   #5
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Default Re: The Limits of Infinity (Irony Recognized)

Isn't infinity just a man made concept for something that has no limit. It cannot be a real quantity by its very definition; it's immeasurable.

Although, infinities are not a fixed size in mathematics. You can have infinities that are greater than other infinities which is just weird.

For this reason, infinity +1 is still infinity and infinity - 1 can be any finite value you want it to be.

There are finite numbers that are so large, we cannot comprehend them. Graham's Number for example could be used instead of infinity and I'll wager that any values calculated with it will produce the same useful data. By this I mean that the decimal value discrepancies would be so small that they would be of little impact to 99.999999999999999% of equations.

However, using Graham's number for these calculations is a pain in the arse as we don't actually know the finite value of Graham's Number. We do however know the last digit of Graham's Number is 7.

It's just simpler to use infinity.
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Old 9th-April-2013, 06:53 PM   #6
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Default Re: The Limits of Infinity (Irony Recognized)

well if you understand time to be a construct we have come up with to try and measure a changing reality, it does exist subjectively, but objectively it wouldn't.

It's funny how scientists don't want to admit that spacetime could be infinite, yet the physics laws we have depend on it because if spacetime were to suddenly end at some point in space, there would exist a portion/bound of reality that is not at all affected by physics and would disprove it to some extent. Such a thing would then only support the idea of God as well, yet scientists are typically atheists. I guess it's like the saying, "Opinions are like assholes, everyone has one".
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Old 9th-April-2013, 07:06 PM   #7
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Default Re: The Limits of Infinity (Irony Recognized)

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well if you understand time to be a construct we have come up with to try and measure a changing reality, it does exist subjectively, but objectively it wouldn't.

It's funny how scientists don't want to admit that spacetime could be infinite, yet the physics laws we have depend on it because if spacetime were to suddenly end at some point in space, there would exist a portion/bound of reality that is not at all affected by physics and would disprove it to some extent. Such a thing would then only support the idea of God as well, yet scientists are typically atheists. I guess it's like the saying, "Opinions are like assholes, everyone has one".
Not really, it would just mean that the current scientific models we have are incomplete and need revising. It happens in science quite a lot.
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Old 9th-April-2013, 08:00 PM   #8
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Default Re: The Limits of Infinity (Irony Recognized)

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Not really, it would just mean that the current scientific models we have are incomplete and need revising. It happens in science quite a lot.
Nope. Having a portion of reality that is immune to change is against the idea of physics.
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Old 9th-April-2013, 08:03 PM   #9
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Default Re: The Limits of Infinity (Irony Recognized)

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Nope. Having a portion of reality that is immune to change is against the idea of physics.
Current idea of physics...
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Old 9th-April-2013, 11:10 PM   #10
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Default Re: The Limits of Infinity (Irony Recognized)

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Originally Posted by Architect View Post
Michio Kaku bugs me for some reason. Mainly because he's knowledgable, but not necessarily right. I differ with him on many points, but his reasonableness is deceptive.

At any rate I'd like to note that while infinity is definitely real in the mathematical sense, I'm not aware of any sightings in reality. Time isn't infinite, or at least doesn't have to be, the universe can end along with Time in a variety of ways. And regardless time appears to have had a beginning so it doesn't go infinitely backwards.

Space isn't infinite, since the Big Bang it's been getting bigger but has an enumerable size.

Division isn't infinite either, it appears that once you get down to the Planck length you find discreetness to the universe.

If I were to place a bet I'd put it on "doesn't exist".
But you, too, seem very reasonable!

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Old 9th-April-2013, 11:47 PM   #11
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Default Re: The Limits of Infinity (Irony Recognized)

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Originally Posted by The Introvert View Post
A quick question to throw out, hopefully to spark some interesting debate.

As a side note I'll accept my position as unofficial philosopher of the forum after stumbling upon a strikingly similar thought process between Thomas Nagel and I. I've actually used
You've got stiff competition.

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this exact comparison when attempting to explain subjectivity and consciousness without knowing he wrote a paper on it years ago. Strange. I digress:
Think of all the philosophers with whom you disagreed.

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To the question!
No. To the Batmobile!

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What exactly does infinity mean?
That depends on the context.

Quote:
Can it actually mean nothing?
No. By definition, infinity does not exist without infinite things.

Quote:
Can infinity be zero?
No. Infinity is the concept used to describe the fact that something does not end, has no external edges, etc. Therefore, infinity, again due to its definition, cannot be zero.

Quote:
The only way I can comprehend infinity is if it implies there is an unlimited amount of possibilities, which means there is no definite answer.
You can also comprehend infinity in knowing that a boundless set of possibilities (or, in mathematics, abstractions) exists.

Quote:
We cannot know anything with absolute certainty, and infinity expresses this beautifully; so much so, that it implies nothing is actually happening.
Non-sequitur.

Quote:
You can't place a point on a number line to infinity. Therefore, there is no point.
Yes you can. Read a math book.

Quote:
If time is infinite, then there is no point in time to which we can point. Therefore, there is no time.
No time means no change, and therefore no debate.

Quote:
If the universe is infinite, then there is no point in the universe to which we can point. Therefore, there is no universe.
This conclusion violates the anthropic principle: if no universe exists, then this conversation (or the hallucination of the same) could not occur.

I know that typology references are technically ad-hom, but your Ni has gotten the better of you. Take a deep breath, turn your Ti on, and see if you can demonstrate these assertions without bending logic.

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Old 10th-April-2013, 01:03 AM   #12
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Default Re: The Limits of Infinity (Irony Recognized)

Are you familiar with integration? It's using an infinite number of finite geometric shapes to calculate area under a curve. That's infinity.
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Old 10th-April-2013, 01:57 AM   #13
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Default Re: The Limits of Infinity (Irony Recognized)

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Are you familiar with integration? It's using an infinite number of finite geometric shapes to calculate area under a curve. That's infinity.
The integral of a curve is knowable only to an arbitrarily large but finite precision.

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Old 10th-April-2013, 05:05 AM   #14
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Default Re: The Limits of Infinity (Irony Recognized)

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Michio Kaku bugs me for some reason. Mainly because he's knowledgable, but not necessarily right. I differ with him on many points, but his reasonableness is deceptive.
I feel the same way about Neil DeGrasse Tyson. I honestly only put the video up because it was pertinent and I remembered seeing it after thinking about this for a while: not because I particularly like Michio Kaku.
Quote:
At any rate I'd like to note that while infinity is definitely real in the mathematical sense, I'm not aware of any sightings in reality. Time isn't infinite, or at least doesn't have to be, the universe can end along with Time in a variety of ways. And regardless time appears to have had a beginning so it doesn't go infinitely backwards.
Yeah, I think that's what I was getting at (I was admittedly exhausted when I created the thread). Nothing in reality could be infinite because, by definition, it's unattainable.

In a philosophical aspect, infinity would mean 'no end' at either spectrum, which I think could be interpreted as nothing. Think about it; if you don't have boundaries, the point would be impossible to find!
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Space isn't infinite, since the Big Bang it's been getting bigger but has an enumerable size.
Yerp.
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Division isn't infinite either, it appears that once you get down to the Planck length you find discreetness to the universe.
Is that assuming that we are certain there's nothing smaller?

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If I were to place a bet I'd put it on "doesn't exist".
Me too... which is ironically the point I made in the OP. It means an unfathomable amount of possibilities, but it's nothing.

Funny how humans can create concepts that logically don't make sense (maybe I'm misunderstanding).
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Old 10th-April-2013, 05:06 AM   #15
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Default Re: The Limits of Infinity (Irony Recognized)

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Originally Posted by Cherry Cola View Post
Everyone and their mom seems to consider space infinite. Surely they must've missed Einstein and gotten stuck on Newtons idea of space in their vain attempts to quantify nothingness.
"IF space is infinite"...

Get your head out of your ass.
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Old 10th-April-2013, 05:12 AM   #16
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Default Re: The Limits of Infinity (Irony Recognized)

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Originally Posted by Hawkeye View Post
Isn't infinity just a man made concept for something that has no limit. It cannot be a real quantity by its very definition; it's immeasurable.
Yerp. I still think it's fun to think about though.
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Although, infinities are not a fixed size in mathematics. You can have infinities that are greater than other infinities which is just weird.
I'm familiar. To be honest, I think it's kind of stupid.
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For this reason, infinity +1 is still infinity and infinity - 1 can be any finite value you want it to be.
Yerp.
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There are finite numbers that are so large, we cannot comprehend them. Graham's Number for example could be used instead of infinity and I'll wager that any values calculated with it will produce the same useful data. By this I mean that the decimal value discrepancies would be so small that they would be of little impact to 99.999999999999999% of equations.
*Googles Graham's number*

Nice, I didn't know that was a thing.
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However, using Graham's number for these calculations is a pain in the arse as we don't actually know the finite value of Graham's Number. We do however know the last digit of Graham's Number is 7.
So it's pointless? Lol
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It's just simpler to use infinity.
Yeah, I understand the usefulness of infinity in mathematics. I've taken a few calc courses, and I have a general interest in Physics. The reason I posted the thread in Philosophy is because outside of math, infinity really doesn't make any sense.

Then I start to wonder about math, and if we are even using a system that can explain what we are trying to explain.

It almost seems as though we need to use some other sort of system to figure out what the Hell is going on in the Universe. I also happen to be incredibly illogical and without data much of the time.
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Old 10th-April-2013, 05:26 AM   #17
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Default Re: The Limits of Infinity (Irony Recognized)

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That depends on the context.
Context in this thread = on a philosophical level; that is, outside of mathematics. Does it mean an incomprehensibly large amount of options, or does it mean an incomprehensibly large number?
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No. By definition, infinity does not exist without infinite things.
What does this mean? I don't understand
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No. Infinity is the concept used to describe the fact that something does not end, has no external edges, etc. Therefore, infinity, again due to its definition, cannot be zero.
Zero neither ends nor starts. It is the absence of possibility. I'm asking if infinity could mean zero, as in the absence of anything, because by definition, it is incomprehensible.
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You can also comprehend infinity in knowing that a boundless set of possibilities (or, in mathematics, abstractions) exists.
Yerp.
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Non-sequitur.
How so?
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Yes you can. Read a math book.
Yeah, I said that wrong. My bad.

If you were asked to pick infinity on a number line, you could not.

Better?
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No time means no change, and therefore no debate.

This conclusion violates the anthropic principle: if no universe exists, then this conversation (or the hallucination of the same) could not occur.

I know that typology references are technically ad-hom, but your Ni has gotten the better of you. Take a deep breath, turn your Ti on, and see if you can demonstrate these assertions without bending logic.
That's kind of the point I was getting at. If time or space were in fact infinite, then it couldn't exist. Therefore, time and space are not infinite.

Ni has influenced much of this, however, :/

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Old 10th-April-2013, 07:56 AM   #18
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Default Re: The Limits of Infinity (Irony Recognized)

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What exactly does infinity mean?
In terms of "what it is", infinity is defined in mathematics, as "that which is bigger than any other number". It might or might not exist. Mathematics doesn't require that infinity exists. We made it up.

In terms of "what it can be used for", infinity is a useful placeholder. It's a concept that might or might not exist. But if you pretend that it does, then a lot of the calculations that we want to make about the universe, become much simpler to calculate. Think of it like answering questions by "infinity did it".

A physicist will never know for sure if infinity exists. But what he will find, is that the phyicist that believes in infinity, will sound totally irrational to him, and yet still get much quicker and more accurate results than he did. This is what Jung meant by intuition. So, infinity is an intuitive concept.

[quote=The Introvert;358188]The only way I can comprehend infinity is if it implies there is an unlimited amount of possibilities, which means there is no definite answer. We cannot know anything with absolute certainty, and infinity expresses this beautifully; so much so, that it implies nothing is actually happening.

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You can't place a point on a number line to infinity. Therefore, there is no point.

If time is infinite, then there is no point in time to which we can point. Therefore, there is no time.

If the universe is infinite, then there is no point in the universe to which we can point. Therefore, there is no universe.
That sounds more like Zeno's Paradox. A different, but related, problem.

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All that could be true, even if infinity didn't exist, and that Michiko Karu sometimes says things that Stephen Hawking wrote over 20 years ago (I remember reading it somewhere), and that Michiko Karu is fun to watch,
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Old 10th-April-2013, 10:26 AM   #19
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Default Re: The Limits of Infinity (Irony Recognized)

Infinity is the void. It is the God of America.

And soon, it will be the God of China.
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Old 10th-April-2013, 11:45 AM   #20
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Is that assuming that we are certain there's nothing smaller?
It means that we believe there can be nothing smaller; there is good evidence to believe that's it. But we could be wrong.
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Old 10th-April-2013, 03:41 PM   #21
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Default Re: The Limits of Infinity (Irony Recognized)

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"IF space is infinite"...

Get your head out of your ass.
Didn't mean you.
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Old 10th-April-2013, 08:48 PM   #22
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Didn't mean you.
My apologies

A bit quick to the punch there, I admit.
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Old 11th-April-2013, 06:23 AM   #23
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Default Re: The Limits of Infinity (Irony Recognized)

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Isn't infinity just a man made concept for something that has no limit. It cannot be a real quantity by its very definition; it's immeasurable.

Although, infinities are not a fixed size in mathematics. You can have infinities that are greater than other infinities which is just weird.

For this reason, infinity +1 is still infinity and infinity - 1 can be any finite value you want it to be.
You can't always use mathematical operators. Each never-ending process is unique, such as the infinite sum that creates pi and the infinite sum that creates e. Those lead to numbers that you could add another number too. But what if the process doesn't converge on a number or value or if you are using infinity to represent a particular infinite set of numbers? Then you don't know what infinity+1 would even mean and saying infinity+1 = infinity is like saying if I can't comprehend 2+1 = 3, I could just say 2+1=2 and call it a day...

Some infinities can be greater than others, but as far as I know that's only in set theory, where some infinite sets have a greater cardinality than others. There are some sets also that Cantor showed are uncountable and it basically amounts to the idea that you can't algorithmically go through an infinite amount of infinite sets (because if you go through one of them, you never get to the others). The real numbers are then uncountable because they involve irrational numbers. His diagnolization argument is used to show that if you attempted to order the real numbers against the natural numbers, you'd always end up with an irrational number that was not included in that ordering. And uncountable sets are always greater than countable infinite sets.

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Current idea of physics...
Sure...but what would that mean if it was real? So you'd have some box or some kind of container that no matter how hard you inflict energy onto it, it would never change. F=ma and thermodynamics get all tossed aside. So if that container is immune to change, how did it get there and so then what's on the other side of the container? God? Then can God manipulate the container? And if so, then the boundary isn't immune to change. Maybe you could argue that there isn't enough energy in the contained universe to break it, but that still wouldn't mean it's immune to change.

I don't know, but could you assert such an idea and still be able to answer these questions in an objective manner? How would you do that? In some respects such an idea would disprove any universality to current physics ideas and I'm not sure that would give people much faith in science anymore. This seems to invoke a kind of paradox whereby its non-existence gives science no definite foundation and people will always be searching for a greater truth, but at the same time if it were to exist, it would leave an aspect to reality that is unexplainable and make science seem unimportant or even silly. As a philosopher, I admit I'm accustomed to the former however and don't mind that one, but find the latter to breed religious ignorance and do not care to entertain such ideas.
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Old 11th-April-2013, 05:45 PM   #24
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Default Re: The Limits of Infinity (Irony Recognized)

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You can't always use mathematical operators. Each never-ending process is unique, such as the infinite sum that creates pi and the infinite sum that creates e. Those lead to numbers that you could add another number too. But what if the process doesn't converge on a number or value or if you are using infinity to represent a particular infinite set of numbers? Then you don't know what infinity+1 would even mean and saying infinity+1 = infinity is like saying if I can't comprehend 2+1 = 3, I could just say 2+1=2 and call it a day...
You seem to have missed the concept of infinity. It is a variable with no limit. This means that adding 1 or any value to infinity will still produce a variable with no limit. We have a name for a variable with no limit and that is... infinity.

∞ + 1 = ∞
∞ + ∞ = ∞
∞ x 2 = ∞
∞ x ∞ = ∞

This has been mathematically proven by the way. I'm not making it up!

Just like if you subtract a value from infinity, you no longer have a variable with no limit and so the answer can be any finite value you want it to be.


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Originally Posted by Reluctantly View Post
Sure...but what would that mean if it was real? So you'd have some box or some kind of container that no matter how hard you inflict energy onto it, it would never change. F=ma and thermodynamics get all tossed aside. So if that container is immune to change, how did it get there and so then what's on the other side of the container? God? Then can God manipulate the container? And if so, then the boundary isn't immune to change. Maybe you could argue that there isn't enough energy in the contained universe to break it, but that still wouldn't mean it's immune to change.

I don't know, but could you assert such an idea and still be able to answer these questions in an objective manner? How would you do that? In some respects such an idea would disprove any universality to current physics ideas and I'm not sure that would give people much faith in science anymore. This seems to invoke a kind of paradox whereby its non-existence gives science no definite foundation and people will always be searching for a greater truth, but at the same time if it were to exist, it would leave an aspect to reality that is unexplainable and make science seem unimportant or even silly. As a philosopher, I admit I'm accustomed to the former however and don't mind that one, but find the latter to breed religious ignorance and do not care to entertain such ideas.
I have no idea how it could work, but that does not mean it couldn't work which was my argument. Currently, there isn't a universal equation that explains everything based on what we already know.

So yeah, there could be a boundary of space that defies the laws of physics we currently have and so we would have to modify our theories in an attempt to accommodate the anomalies.

Think of it like the rules of chess. (watch video)

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Old 12th-June-2013, 12:08 AM   #25
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Default Re: The Limits of Infinity (Irony Recognized)

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Just like if you subtract a value from infinity, you no longer have a variable with no limit and so the answer can be any finite value you want it to be.
This is incorrect.

It's still infinity; infinity is a concept, not a number.
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Old 14th-June-2013, 09:57 PM   #26
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Default Re: The Limits of Infinity (Irony Recognized)

In response to your belief that infinity represents "non-existence", I would like to say that you should please recheck what you define to be infinity. Infinity is a concept that represents anything with no end or beginning. As you referred to time and the universe as infinite, I believe that this would be correct. However, infinity does not represent something not existing. For example, the universe being infinite does not represent that "there is no universe", it simply explains that there is no point to the universe. The universe exists, as we can clearly see. However, there is no point of the universe, or of time, or of space, or of us for that matter of existing. The universe will continue; time will continue, and space will continue, so what is the point of having them? There is no point.

But, they exist anyways.
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Old 14th-June-2013, 11:12 PM   #27
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In response to your belief that infinity represents "non-existence", I would like to say that you should please recheck what you define to be infinity. Infinity is a concept that represents anything with no end or beginning. As you referred to time and the universe as infinite, I believe that this would be correct. However, infinity does not represent something not existing. For example, the universe being infinite does not represent that "there is no universe", it simply explains that there is no point to the universe. The universe exists, as we can clearly see. However, there is no point of the universe, or of time, or of space, or of us for that matter of existing. The universe will continue; time will continue, and space will continue, so what is the point of having them? There is no point.

But, they exist anyways.
But there must be cause and effect. Our entire universe revolves around that concept. Maybe I'm just stupid, I don't know. But it seems to me that for something to exist, there also has to be nothing.

Maybe that just means that there is no cause for everything. I don't know. Maybe 'nothing' is the reason there is 'everything'? That can work for both you and I.
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Old 15th-June-2013, 12:35 AM   #28
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Default Re: The Limits of Infinity (Irony Recognized)

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But there must be cause and effect. Our entire universe revolves around that concept. Maybe I'm just stupid, I don't know. But it seems to me that for something to exist, there also has to be nothing.

Maybe that just means that there is no cause for everything. I don't know. Maybe 'nothing' is the reason there is 'everything'? That can work for both you and I.
The possibility that nothing must exist for everything that exists today to be present is interesting, I agree. However, I think that we must delve into the existence of "nothing" (which could, by the way, represent "no existence") and what exactly that would represent in order to properly hypothesize this statement.

But, I believe that your cause and effect statement is represented more accurately by the terms, "our entire HUMANITY revolves around that concept". You see, despite the fact that humans have made several theories and hypotheses of how exactly the world and universe exist, these predictions don't necessarily have to be followed by the universe itself. Based upon humanity's knowledge, there must be cause and effect. However, humanity does not know of the origin of the universe. And, since this engima continues to perplex us, it does not necessarily have to adhere to cause and effect. It may simple BE. It does not have to be created or destroyed. And, of course, based on our primitive knowledge, we have actually shown that there must be something for something else to come of it, and this postulates that there must be an origin- a creation from nothing. But, once again, our assumptions are primitive (in the most forgiving words I can express), and thus may not even be close to correct.


However, I do acknowledge that your thoughts may have a possibility of being true. This cannot be proven until we discover the origin of the universe; until then, we must assume that I am correct, since there is no corroboration evidence of origin, and my assumption has not been disproved.
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Old 15th-June-2013, 05:51 AM   #29
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Default Re: The Limits of Infinity (Irony Recognized)

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And, since this engima continues to perplex us, it does not necessarily have to adhere to cause and effect. It may simple BE. It does not have to be created or destroyed.
That's what I said!

"maybe nothing is the reason there is everything"

That's what I was trying to say here. When the question is EVERYTHING (which may encompass even more than just our universe, mind you), then the cause would be NOTHING. It just is.
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And, of course, based on our primitive knowledge, we have actually shown that there must be something for something else to come of it, and this postulates that there must be an origin- a creation from nothing. But, once again, our assumptions are primitive (in the most forgiving words I can express), and thus may not even be close to correct.
This could also be correct! I don't know the answer.
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However, I do acknowledge that your thoughts may have a possibility of being true. This cannot be proven until we discover the origin of the universe; until then, we must assume that I am correct, since there is no corroboration evidence of origin, and my assumption has not been disproved.
What is your assumption? First quote?
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Old 15th-June-2013, 06:39 AM   #30
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Default Re: The Limits of Infinity (Irony Recognized)

@ The Introvert
Pardon my misunderstanding. I understood your nothing to mean "nothing" - as in no existence of anything at all. Simply a void of existence.

In your case, you meant that nothing was -- there is no cause. Understood.

As for my earlier statement-- "However, I do acknowledge that your thoughts may have a possibility of being true. This cannot be proven until we discover the origin of the universe; until then, we must assume that I am correct, since there is no corroboration evidence of origin, and my assumption has not been disproved." -- Yes, I was referring to your statement that existence originates from essentially, a lack of "something".

Can you please specify what exactly you are defining "nothing" as? Is it a lack of elements? compunds? solid objects? simply anything and everything that makes up what exists?

PS: you may want to clarify your statement on the cause of everything is nothing. I apologize, but the diction you use can be misrepresentative.
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Old 15th-June-2013, 06:52 AM   #31
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Default Re: The Limits of Infinity (Irony Recognized)

Also, in addition to that, just because there is no cause and effect does not specify that there is no existence. Existence does not require the aid of cause and effect to, well, exist.

-Sorry to bring religion into this but, (I am just referring to some of the major religions) is there a cause that resulted in God?
-If Big Bang was the cause and the universe was the effect, then the effect of the Big Bang would have been caused by certain molecular interactions that resulted in the explosion. Continuing, molecular interaction occurred because of movement of existing molecules. The existence of molecules was caused by what, then?
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Old 15th-June-2013, 12:33 PM   #32
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Default Re: The Limits of Infinity (Irony Recognized)

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This is incorrect.

It's still infinity; infinity is a concept, not a number.
No. I think you'll find that "infinity - 1" is actually classed as undetermined.

Basically, it's a math error that has an identical outcome to dividing by zero. It can be any value. Therefore the answer is not infinity.

It's the precise reason why it's called a math error because it breaks the rules.
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Old 15th-June-2013, 05:51 PM   #33
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No. I think you'll find that "infinity - 1" is actually classed as undetermined.

Basically, it's a math error that has an identical outcome to dividing by zero. It can be any value. Therefore the answer is not infinity.

It's the precise reason why it's called a math error because it breaks the rules.
Regardless, it still isn't any finite number you want it to be, as you initially proposed.

Undefined doesn't mean: "oh, I want this to be 6." No. It just isn't possible.
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Old 15th-June-2013, 05:54 PM   #34
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Can you please specify what exactly you are defining "nothing" as? Is it a lack of elements? compunds? solid objects? simply anything and everything that makes up what exists?
The last one, in reference to my initial thoughts.

But again, what I'm trying to say now (after revelation) is that 'nothing' would be the reason there is 'everything'. So it wouldn't be anything. Everything just is. So there's no reason (and no way) you could even define it.
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PS: you may want to clarify your statement on the cause of everything is nothing. I apologize, but the diction you use can be misrepresentative.
I know. It's almost intentionally so, because when talking philosophy I like to leave a lot of open strings hanging around.
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Old 15th-June-2013, 05:59 PM   #35
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Default Re: The Limits of Infinity (Irony Recognized)

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-Sorry to bring religion into this but, (I am just referring to some of the major religions) is there a cause that resulted in God?
There could be. Depends on how large your definition of God is. If everything ever was God, then no. If the creator of just one universe (assuming that there are many universes or even just two) is your definition, then I think that something would have had to create that God.
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-If Big Bang was the cause and the universe was the effect, then the effect of the Big Bang would have been caused by certain molecular interactions that resulted in the explosion. Continuing, molecular interaction occurred because of movement of existing molecules. The existence of molecules was caused by what, then?
If all that there is is our universe, then it just is. I happen to believe that either:
a) scientists have it wrong, and there's time before the big bang that we don't understand yet (because you wouldn't be able to trace back before it)
b) the particles came from another place (be it another dimension, God, it really shouldn't matter)

At the end of either of these statements, if you followed the rabbit trail to the conclusion, you would find that everything is (including God, or no God. It's irrelevant either way, mostly [unless you believe in reincarnation or heaven or something]).

The beginning and the end are meaningless either way.

That doesn't mean we can't subjectively make it meaningful (and exciting, fun, etc. though).
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Old 16th-June-2013, 12:47 AM   #36
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At the end of either of these statements, if you followed the rabbit trail to the conclusion, you would find that everything is (including God, or no God. It's irrelevant either way, mostly [unless you believe in reincarnation or heaven or something]).

The beginning and the end are meaningless either way.

That doesn't mean we can't subjectively make it meaningful (and exciting, fun, etc. though).
I think that both of us are trying to point out exactly the same thing to the other. I completely agree and support your first statement.

And, as to your beliefs that God/ particles came from some place else, the chain would continue on and on; the beginning is not clear at all.
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Old 16th-June-2013, 01:25 PM   #37
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Default Re: The Limits of Infinity (Irony Recognized)

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Regardless, it still isn't any finite number you want it to be, as you initially proposed.

Undefined doesn't mean: "oh, I want this to be 6." No. It just isn't possible.
You appear to have missed the point.

Mathematically, ∞ - 1 can be any value (there is a proof floating around that explains why), but this creates paradoxes.

This is precisely why we say that the answer to ∞ - 1 is undetermined or more appropriately indeterminate

In other words: the value can literally be anything we want it to be, so we shall simply say it's ambiguous.

This has nothing to do with possibility as we are talking about a theoretical concept that doesn't actually exist in reality.

The equation has as much use as dividing by zero; it's completely useless.
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Old 16th-June-2013, 03:43 PM   #38
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Default Re: The Limits of Infinity (Irony Recognized)

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You appear to have missed the point.

Mathematically, ∞ - 1 can be any value (there is a proof floating around that explains why), but this creates paradoxes.

This is precisely why we say that the answer to ∞ - 1 is undetermined or more appropriately indeterminate

In other words: the value can literally be anything we want it to be, so we shall simply say it's ambiguous.

This has nothing to do with possibility as we are talking about a theoretical concept that doesn't actually exist in reality.

The equation has as much use as dividing by zero; it's completely useless.

∞ - 1

So because it's an arbitrary value, it could theoretically be anything, however, because it's a theoretical construct in the first place, it doesn't even exist.

I have always looked at it as n/0=

Regarding asymptotes: remember the wavelength & hearing thread? I'm not sure if you caught my post where I said action potentials are like asymptote waves?
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Old 16th-June-2013, 06:52 PM   #39
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∞ - 1

So because it's an arbitrary value, it could theoretically be anything, however, because it's a theoretical construct in the first place, it doesn't even exist.
My point was that Introvert was implying ∞ - 1 = 6 wasn't possible when in fact it is, but it's completely pointless to say so.

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I have always looked at it as n/0=
Whilst I see what you are saying, this mathematical equation is incorrect. The actual answer is indeterminate (a jazzy word for completely pointless). There is no real solution.

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Regarding asymptotes: remember the wavelength & hearing thread? I'm not sure if you caught my post where I said action potentials are like asymptote waves?
I do, but I didn't like the thought of averaging it out on a time-amplitude graph. To me this makes no sense. It would have been better if we were using a spectrogram.
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Old 16th-June-2013, 07:41 PM   #40
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I do, but I didn't like the thought of averaging it out on a time-amplitude graph. To me this makes no sense. It would have been better if we were using a spectrogram.

mmm but I'm talking about Action Potentials in general, not specific to auditory processing (like it even makes a difference).

I was altogether disinterested in the character of the sound wave, to me, the perception thereof is what is important/relevant/interesting.
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Old 17th-June-2013, 01:16 AM   #41
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mmm but I'm talking about Action Potentials in general, not specific to auditory processing (like it even makes a difference).

I was altogether disinterested in the character of the sound wave, to me, the perception thereof is what is important/relevant/interesting.
Ah yes. My apologies, I typed my last post in haste before I set off to work and only partly read your last sentence.

Action Potential discharges do indeed look like asymptote waves. I imagine they do eventually discharge back to a very similar resting state given time.

In theory, you could zoom in on the discharge wave as much as you wanted to get a more accurate reading. In reality, we are obviously limited to the resolution to our tools.

However, there also becomes a point where the resolution is simply too high for the extra accuracy to mean anything. Our brains certainly don't account for infinitely small discharges. They reach a threshold and then simply say "I don't care about anything lower".
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Old 2nd-December-2016, 05:18 AM   #42
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Default Re: The Limits of Infinity (Irony Recognized)

Infinity =something that has no end.

Infinity = something that has no limit

infinity = something that can increase forever.


Hence if we find an endpoint, the infinite concept breaks apart.

space and distance gives us the perception of infinity, and hence could be infinite.

time and energy could be infinite, but that may be false.
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Old 13th-January-2017, 02:28 AM   #43
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Default Re: The Limits of Infinity (Irony Recognized)

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Can infinity be zero?
Here's a silly proof that there are infinite numbers between zero and zero.

Between 0 and 1 there are infinite numbers
If there are infinite numbers between 0 and 1/n (n a positive integer), then there are infinite numbers between 0 and 1/(n+1), so there is infinite numbers between 0 and 1/n for any positive integer n
The limit of 1/n as n goes to infinity is 0
So there are infinite numbers between 0 and 0
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Old 13th-January-2017, 11:38 AM   #44
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Default Re: The Limits of Infinity (Irony Recognized)

No, there aren't infinite numbers between 0 and 0, there are no numbers between any two identical numbers because the distance between them is defined to be exactly 0, if there were any nubmers between 0 and 0, then that second 0 wouldn't be 0, that's just nonsense.

What you're getting at is the mathematical idea of an infinitesimal, some mathematicians like them, some hate them, and you can read about them if you want to know what you were talking about.

The idea of infinite subdivision into new categories isn't very practical because it doesn't fundamentally change the maths. If you infinitely subdivide numbers from 0 to 1, it's not at all different from assuming all natural numbers and calling infinity "1". Unnecessary mental gymnastics that doesn't say anything new about the nature of infinity imo.
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Old 17th-March-2017, 01:00 AM   #45
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Default Re: The Limits of Infinity (Irony Recognized)

You can't use a division to proof infinity between 0 and 0. Beacuse infinity (in math) is no number. Infinity in that case (n/infinity) just means that for every larger number for n, the value is smaller. And there is ALWAYS a larger value, it doesn't even matter wich number you choose. Because positive integer numbers are infinite.

Now, defining infinity? Hard.... but have you guys watched to vsauce videos? He describes infinity not as a number, but as a whole. And with two kinds of infinity: countable infinity and uncountable infinity. The main difference between each is that in countable infinity you can define some intervals between the components of infinity (ie, integers are countable infinites, because you can define intervals between 1, 2, 3, 4.... and so on) but uncountable infinity just can't be defined in intervals, like the real numbers. I mean, there's an infinite amount of real numbers in between 0 and 1, or 0 and 0.0000000001, or 0 and whatever, and that's why it's uncountable.

Infinite universe? Nah. Incredibly huge, yes.

EDIT: the video I was talking about

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Old 17th-March-2017, 04:30 AM   #46
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Default Re: The Limits of Infinity (Irony Recognized)

Oh, I guess I missed Hawkeye's dialogue after I posted...

Well, Infinity in mathematics just means that you are doing recursion without end. It's a symbol denoting an endless algorithmic process and has no association with numbers.

Though some endless recursions do converge on a particular number. But that's a particular recursive process and not infinity itself; for example the limit of e^-x as x increases endlessly is 0. I think the confusion is when people study improper integrals. It's common to see something like this


She treats ∞ as a number in her equations because it's intuitive to think of it that way. We see ∞ and think it is the biggest number that a number can be and it serves its purpose in solving the equation and conceptualizing what you are doing. But really she is taking the limit as her variable "a" increases endlessly.

Basically, if something is the largest or smallest it can possibly be, that's completely different than the process of infinity (or even the idea of an endless set or collection of things). I'm just saying because when I see ∞ + 1 = ∞ or n/0 = ∞ I cringe because it makes zero sense to do that. It's like saying "driving to the market to buy milk" + 1 = "driving to the market to buy milk". WAT?! It's just not a number.



TLDR; infinity is an endless process (or could even be thought to be a collection or set of endless things - I think this is known as ?Actual Infinity?), but it is simply not a number.
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Old 17th-March-2017, 05:19 AM   #47
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Default Re: The Limits of Infinity (Irony Recognized)

Oh, but n/0 (and assuming n is not zero or negative):

If you take the limit as x increases endlessly in n/(1/x), it would approach n/0 and you'd get n/0 = n * (the largest number possible).

But then the largest number possible wouldn't be the largest number possible because n * (the largest number possible) > (the largest number possible). It really doesn't make any sense, does it? Then n/0 != (the largest number possible) because the largest number does not exist for n/0.

But if n is 1, I guess you could say 1/0 = (the largest number possible). However, if it is a number then mathematical operators apply (yes?). Then 4 * (the largest number possible) should be a larger number again, which it can not be. So I suppose n/0 can't be a number either.

So n/0 isn't the largest number possible and it isn't a number either. Then what is it?
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