Yesterday one my friends was saying something about how he read in a book that the infinity of values between 0 and 1 is smaller than the infinity of values between 0 and 2 (0.0000004 etc). I couldn't make sense of this, and thus we argued for 90 minutes about it and finally consulted our geometry teacher who agreed with them. I knew there was something about different types of infinity so I did a brief search and figured out that came into play sometime in Calculus which would probably melt my brain if I tried to figure it out, but if I'm wrong it probably has something to do with that. My logic behind it is something cant be greater than infinity, because then it wouldn't be infinity to start with. Also, there is an infinite number of values between 0 and 1 (or even 0 and .1) and there is an infinite number of values between 0 and 2. Unless there is something like infinity level 2 or some kind of infinity value ranking system which I've never heard of, infinity is infinity. Then we got into this argument over infinity itself and they said how if you put a dollar in a bank that will last forever, the dollar would be an infinite value due to interest. I retaliated, a dollar cant be infinity because 2 is greater than 1 and nothing is greater than infinity and that dollar wouldn't suddenly become 2 dollars at least for awhile, then we went on into infinity expanding at constant rate or not or if it expands it all and I developed my own little theory on how it expands but I haven't consulted the internet yet to see if it does/if I'm right. It goes like infinity expands whenever something challenges it being the greatest value, for example if you had an infinite supply of pie, but there was only one pie, whenever you needed say 5 pies that pie would turn into 6 pies so now matter how much you took from it would always be there. And if you said "Pie, you aren't infinite because 2 is greater than one and you are one pie!" the pie would turn into 2 instantaneously or perhaps before the question was even asked so that claim would be false etc. So anyways, how do you think of any of these ideas because I'm pretty sure I don't have it quite right but the whole "one infinity is greater than the other thing" makes absolutely no sense to me. Thanks.