LRT: The idea of adding to infinity ("you can't do it, you'd still be adding when the sun went out") has me thinking of that short story I wrote where an immortal being trapped in an endless void tries to count to infinity to pass the time and eventually runs out of named numbers
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You keep going - natural numbers, rationals, algebraic numbers, constructible numbers...then you hit the computable numbers, and realize you're not even close to getting the reals.
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*Moreover*, the term "almost all" is still used this way when we jump up a level from countable to uncountable infinity Almost all real numbers are non-integers, almost all real numbers are irrational, almost all real numbers are non-constructible, non-algebraic, non-analytic,
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And indeed almost all real numbers are non-computable I.e. almost all real numbers cannot be named using the rules of arithmetic, geometry, algebra, calculus Even if you had an infinitely large universe and infinite time, almost all of them can't be expressed *in principle*
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