__What do you know about infinity?__

Infinity means never ending, something that is infinite goes on forever. There are infinite numbers, they just keep going on and on.

__How can you explain/makes sense of different sizes of infinity?__

Even though an infinity has a never-ending number of numbers they have different sizes. The group of natural and whole numbers have an infinite amount of numbers, but the group of whole numbers is bigger since it has 0 and natural numbers don’t. Similarly, integers are double the size of whole numbers since it contains the opposite of each number, they are both infinities, but one is double the size.

__What are countable infinities? What are non-countable infinities?__

A countable infinity can be counted, like the whole numbers. You can count 0, 1, 2, 3, 4…. If you wanted, you could keep going on forever. Counting all the decimals would not be countable, you would never reach one since there are infinite decimal places.