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Hundreds of thousands of mathematicians are wrong. No. No natural number has an infinite number of digits, and you are wrong. If you weren't, of course, it w
by dogecoinbase 9y ago
Hundreds of thousands of mathematicians are wrong.
No. No natural number has an infinite number of digits, and you are wrong.
If you weren't, of course, it would be easy to prove me wrong -- simply name the natural number to which the successor function is applied that results in a "transfinite" number, whatever that is.
- ColinWright 9y agoBe careful, there are such things as transfinite numbers, and they are well-founded. They let us do wonderful things like transfinite induction, and to prove, for example, that Goodstein's Theorem is true, even though it's unproveable in Peano Arithmetic. But transfinite numbers are not "natural numbers", they are not in the set N, they don't have infinitely many digits, and in the context of this thread, they are a red herring.
- dogecoinbase 9y agoI'm fine with nonstandard models; my scare quotes on "transfinite" were more to emphasize that the term was being used without basis or definition.