why is there an infinite amount of numbers between 1 and 2, but none of them include 3?

Question

and why does it have a beginning and an end and a middle if it’s infinite

In: 0

Answer 1

Because 3 is bigger than 2 so isn’t part of “between 1 and 2”. But there are 3s in decimal places, such as 1.3, 1.03, etc.

It’s infinite because just as there’s a middle (1.5), there’s a middle of that on each side (1.25, 1.75). And those have middles. And those and those, and those, on for infinity.

You can think of it as 1 + 1/x where x is any number from 1 to infinity. So infinite. (If you have x < 1 then you’re out of your 1 to 2 range.)