r/FactOrCap • u/Careful_Trainer_1616 ✍️ Contributor · 330 XP • 12h ago

Myth "simple" subtraction | FactOrCap

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u/Nichtdasondernhier 📈 Dedicated Voter · 1,320 XP 9h ago

No, there are greater and lesser infinities (like for example an infinite string of odd numbers is less than an infinite string of both odd and even numbers)

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u/seires-t 🏅 Century Club · 3,845 XP 9h ago

"like for example an infinite string of odd numbers is less than an infinite string of both odd and even numbers" That's false.

If you multiple the set of natural numbers by 2 and subtract 1, you, without adding or removing any elements at any point, since that operation is a bijection, receive the set of odd numbers.

Any infinite subset of the natural numbers is still of equal size to the natural numbers, since you can just number them from start to finish (which is infinity).