How can this (math) be?

[tw]

Originally Posted by Clodfobble

Thus the set of all infinite sets does have a one-to-one correlation with an infinite set as long as you count it this particular way.

I was not discussing the size - number of elements in the infinite set. I was discussing the value of both infinities. The first 'one to one' element is larger than the first element of that second set called infinity. 1 ≠ 2. Second item in each set: 2 ≠ 4 . This continues into infinity. In each case - each one to one correspondence - the two infinities (∞) will never be equal because one set starts with 1 and the other starts with the larger number 2.

In which case ∞ + 1 which does equal ∞ actually defines two different sets - both called ∞.

Meanwhile, what is the answer to Shocker's 'cool math trick'. Where is the overlooked restriction in his algebra?