Re: 2N=E

WM has brought this to us :

On 24.10.2024 14:24, FromTheRafters wrote:

WM has brought this to us :

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The infinite must adhere to correct mathematics. Otherwise it is only matheology, to be believed by believers who despise mathematics.

 Sets don't change. If you want to double each element of the naturally ordered set of natural numbers you do it by creating another set with the naturally ordered doubled elements.
 {1,2,3,4,...}
{2,4,6,8,...}
 These sets are the same |size|

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In fact, here "the same size" applies. The change of size between both sets is +/- 0. But since the first set contains all natural numbers, the second set contains larger numbers because 2 > n.

So what?

your swapped Bob is *always* in the 'next' room since there is no 'last' room at the infinite hotel.

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But if all fractions can be counted, then there is a last state, namely when this is counting is complete.

Countable does not mean counted. Elements of finite sets can be counted and are countable, elements of infinite sets are countable but cannot be counted. That is why both finite sets and infinite sets use bijections instead of actual counting to determine size.

Scrooge McDuck gets richer and richer as he goes broke.

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He does never lose more money than he gets. Therefore he cannot lose all his money. *That* is dictated by logic.

Neither can he get infinitely rich.