- #1

thinkandmull

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Dear friends, I was wondering if someone can explain how Cantors diagonal proof works.

This is my problem with it. He says that through it he finds members of an infinite set that are not in another. However, 2 and 4 are not odd numbers, but all the odd numbers equal all the whole numbers.

If one to one correspondence works such that you can line up all the odd numbers and start with all the whole numbers and say "they start at the same place, and they go to infinity so they are equal", why can't we do this same trick with the "bigger infinities". If they are made up of members, the members can be lined up and "set off" into infinity, and the result would be that all infinities are equal.

Where am I going wrong with this? Thanks

This is my problem with it. He says that through it he finds members of an infinite set that are not in another. However, 2 and 4 are not odd numbers, but all the odd numbers equal all the whole numbers.

If one to one correspondence works such that you can line up all the odd numbers and start with all the whole numbers and say "they start at the same place, and they go to infinity so they are equal", why can't we do this same trick with the "bigger infinities". If they are made up of members, the members can be lined up and "set off" into infinity, and the result would be that all infinities are equal.

Where am I going wrong with this? Thanks

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