What do you know about infinity?
Currently, what I now is that there can be different sizes of infinity, and although it makes your head hurt, it is possible to somewhat calculate infinity. I also know that there is a way to have infinity as a sign in some formulas, however what I do not know is how to calculate the formulas. That is something that I wish to learn.
What new things have you discovered?
Before, all I thought infinity was was just some sort of way to explain the fact that numbers can go on forever, just to not make our brains hurt. Then, I saw it as a sign in a formula and I realized that it actually meant a lot more than just that. What I discovered is that there are many ways to measure infinity. Although it is “infinite” and can go on forever without a clear ending, there are a lot of interesting and mind-blowing ways that I learned that mathematicians have created so that it is easier to calculate infinity.
How can you explain/makes sense of different sizes of infinity?
For me, it is a little easier now to wrap my head around the fact that infinity can be different sizes, so how I make sense of it is that I imagine people just picking up handfuls of numbers, just like when I pick up sand, because the number of sand pebbles are almost, or at least they seem, infinite. I can pick up different sizes of sand handfuls, so that must mean that I can “pick up” many different sizes of infinite numbers, too.
What are countable infinities? What are non countable infinities?
From what I have understood, a countable infinity is basically all the numbers that you can count, or at least the numbers that you can imagine in a pattern (like if you were to double every number, you can imagine the answers). Non-countable infinities are all the other infinities that are usually either impossible to count, or they are so long that it would take forever to figure them out.
What questions do you still have about infinity?
I think that my only question about infinity is how many different was there are to “measure” infinity. I learned quite a few that I though were quite interesting, however I know that with the numerous amount of mathematicians who have tried to count infinity, there must be millions of ways to do it.