Is infinity bigger than infinity+1?

Question

Is infinity bigger than infinity+1?

In: 1

Answer 1

There are different types of infinity with different sizes but Infinity +1 is the same size as infinity.

It comes down to being able to map the different sets of numbers onto each other. Adding plus 1 is trivial to map to existing infinite set.

You get into stuff like aleph numbers and things like that if you look for large infirmities, but all the countable stuff like integers, or rational numbers is all the same size. Adding a single element won’t make any of them bigger than the others. In fact adding infinitely many of them won’t make them bigger either.