How are some infinities bigger than others?

Question

This one has got me.

I’m reading a book at the moment that mentioned very briefly that some infinities are bigger than others. The book is unrelated and the author dedicated all of one sentence to the fact – but it’s blown my mind!

I’ve always thought (pretty sure I was always taught) that infinity just is. Something is infinite if it goes on forever, but how can something go on forever more than another?

I’ve tried to google but I’m just not grasping it. How is it that one infinity can be bigger than another?

In: Mathematics

Answer 1

You can get infinitely small-grained between 1 and 2 (like 1.000000000000000000000000000001). You can do the same thing between 1 and 3, which gives more options.