A fair distinction...
I guess what I am asking is..Cant we tweak the definition a little bit? Add a little INformality to our formal system?
Not because we HAVE TO... but because we WANT TO. For the sake of thought and conceptual innovation.
It might not have any bearing on the reality which...
So what about values which are not defined by our classic mathematical language?
Consider the paradox:
"Does a set of all sets contain itself?"
At first glance the answer is an obvious "yes" ...until you set up a mathematical equation for it, which would look something like this:
" N = N...
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