Postby **NMB** » 21 Jun 2018, 23:26

Pansy Puff wrote:Positive Passion wrote:Pansy Puff wrote:An example to show the problem with your disproof.

The set S ={1, 2, 3,...} is infinite in size. If I remove all the odd numbers then surely I have a set of numbes that is smaller,

E ={2, 4, 6, ...} .After all, I have removed every other number.

But if I take set S and double every number then I get the same set of numbers E ={2, 4, 6...} But if I doubled every number the set must be the same size as S.

So I have shown that S and E are the same size, and that S is "twice as big" as E.

Huh? Surely half infinity is still infinity. As is twice inifinity.

Which infinity are you talking about? Some infinities are bigger than others.

https://en.wikipedia.org/wiki/Aleph_number

So my infinity plus one can be bigger than your infinity and my disproof stands.

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