– How can some infinites be bigger than others?

Question

I have just come across the concept that there are different types of infinite numbers (whole integers, irrational numbers etc.) and the concept that for example, the amount of irrational numbers between 0 and 1 is higher than the amount of whole numbers from 1 to infinity.

I guess I just don’t understand how an infinite amount of something can be bigger/smaller than an infinite amount of something else…

Please un-f**k my brain 😀

In: 4

Answer 1

Let’s consider the series that happens when you add one to the preceding number: 1, 2, 3, 4, 5, 6, 7, etc. etc. etc.

We know this series will go on to infinity. We also know that we can calculate it’s discrete value at any point along the way.

So far so good?

Now let’s compare that to the series where we double the preceding value: 1, 2, 4, 8, 16, 32, 64, 128, etc. etc. etc.

We know that this series will *also* go on to infinity, and we can calculate a discrete value at any point along the way.

Which of these two series is “bigger”? Again, we know that both will continue to infinity, but one of these definitely approaches infinity at a *much faster rate* than the other.