The size of infinities

Can one infinity be larger than another? Is for example the set of negative integers larger than the set of positive integers?

To which set of integers do you assign the digit zero?

As infinity itself is undefined, the answer to your question must also be.

The only creature which can definitively answer your question is Schrödinger's cat.

Okay, I'm through.

It's a long time since I was in college, but the short answer is (I think) that some infinities are, in some sense, bigger than others - but it's a tricky subject. For example, some infinities are countable and some are not. I would say that that means, somehow, an uncountable infinity is "bigger" than a countable one. But on the other hand, infinite is infinite. There are just as many even numbers as there are odd numbers, and the same number of all integers (because all those sets are infinite and countable).

But it's 40 years since I had to think about this stuff.

Is zero considered an integer?

Zero is an integer. But there is disagreement as to whether it should be considered a member of either the positive or negative set, or neither.

Mathematicians really are a different breed than the rest of humanity.

Mathematicians Bridge Finite-Infinite Divide

Fuck me if I can follow that.

Ditto.