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Originally Posted by dar512
That's not the way I learned it all those years ago in HS. I learned ∞ + 1 = ∞. These guys agree with me. |
I don't know what you read. But when I read their citation, your concept of ∞ does not agree with what "These guys" say.
Some quotes from that website are
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If we want to say that infinity times infinity is bigger than infinity, then we have to show how the set with infinity-times-infinity members (the rational numbers) cannot be put into a one-to-one correspondence with the set that has an infinite number of members (the counting numbers). ...
Cantor's work revealed that there are hierarchies of ever-larger infinities.
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These things are so obvious they seem silly. However, if we want to know the size of an unknown quantity, but the counting task is tricky, we can try to put the unknown quantity in one-to-one correspondence with some known quantity. This is the strategy that Georg Cantor used to compare different sizes of infinity.
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Did you understand their story of Hotel Infinity?
We have two sets. Set A = {1, 2, 4, 8, 16, 32 ...}. Set B = {2, 4, 8, 16, 32, 64 ...}. Two examples of infinity. But to be equal, then 1 = 2; 2 = 4; 4 = 8; etc. Clearly they are not equal. IOW we have two different sizes of infinity.
But again, some defining condition in the original problem 1) is violated and 2) causes 2∞ + 1 = ∞ . I just don't see the algebraic mistake because I do not see the violated restriction.
Yes, ∞ + 1 = ∞. But they are not the same size ∞. Shall we talk about Schrodinger's Cat? It's a weird, weird, weird world. Fortunately, when it makes no sense, we can go out back and urinate on the bible. Then things change.