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A comment on Is infinity an odd or even number? (2011). Parent comment

Re:Is infinity an odd or even number? (2011) by daef on Tuesday May 02, 2023 @10:26AM (#35787965)
You can uniquely map all rationals onto the natural numbers, thus they are of the same quantity. That doesn't work for all real numbers thou.
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Re:Is infinity an odd or even number? (2011) by warent on Tuesday May 02, 2023 @10:29AM (#35788005)
Oh right this is only true for irrational and transcendental numbers
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Re:Is infinity an odd or even number? (2011) by aimor on Tuesday May 02, 2023 @01:09PM (#35790823)
Maybe this is misguided cheat, but couldn't you map any real number (between 0 and 1) to a natural number by mirroring the decimal digits across the decimal point. So 0.123 -> 321, but also sqrt(2)/2 -> ?601707 where ? is the rest of the decimal representation. This creates infinitely large numbers, but it's still a 1-to-1 mapping.
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Re:Is infinity an odd or even number? (2011) by dangond on Tuesday May 02, 2023 @02:44PM (#35792299)
Unfortunately, numbers with infinitely many digits are not natural numbers. You cannot count to ?601707, even with an infinite amount of time.
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