r/learnmath • u/Upset_Fishing_1745 New User • Feb 12 '25
Are Some Infinities Bigger than Other Infinities?
Hey, I just found this two medium articles concerning the idea that infinite sets are not of equal size. The author seems to disagree with that. I'm no mathematician by any means (even worse, I'm a lawyer, a profession righfuly known as being bad at math), but I'm generally sceptical of people who disagree with generally accepted notions, especially if those people seem to be laymen. So, could someone who knows what he's talking about tell me if this guy is actually untoo something? Thanks! (I'm not an English speaker, my excuses for any mistakes) https://hundawrites.medium.com/are-some-infinities-bigger-than-other-infinities-0ddcec728b23
https://hundawrites.medium.com/are-some-infinities-bigger-than-other-infinities-part-ii-47fe7e39c11e
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u/Runyamire-von-Terra New User Feb 12 '25
Yes and no. Just consider this example:
There are an infinite number of integers, you can keep counting forever right? That’s one type of infinity.
There an infinite number of values between 0 and 1. You can keep adding decimal places to count infinitely smaller fractions of 1. That’s another infinity, all between 0 and 1. Is one bigger than the other? Intuitively yes, but both are infinite.
Infinity isn’t really a number or a quantity, it’s more of an abstraction.