Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?

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Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?

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Anonymous 0 Comments

The way I recall my mathematician friend explain it was like so:

Let’s look at the space between 0 and 1. What would be the middle of 0 and 1? That would be .5. What would be the middle of 0 and .5? .25. Then you can keep halving it forever, and you’ll find that between 0 and 1 there is an infinity.

Now, let’s look at whole numbers. We can count 1, 2, 3, and so on forever. It’s another infinity, except now we he have the inifities between 0 and 1 and 2 and 3 and so on. An infinity of infinities. The infinity of whole numbers is bigger than the infinity between 0 and 1.

At least that was my understanding!

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