I cannot understand how there are “larger infinities than others” no matter how hard I try.

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I have watched many videos on YouTube about it from people like vsauce, veratasium and others and even my math tutor a few years ago but still don’t understand.

Infinity is just infinity it doesn’t end so how can there be larger than that.

It’s like saying there are 4s greater than 4 which I don’t know what that means. If they both equal and are four how is one four larger.

In: Mathematics

34 Answers

Anonymous 0 Comments

I think the easiest way to think about this is to think of dimensions. Say you have a line that goes on to infinity. That’s one dimension of infinity. Now add another dimension to that. Thats infinity times infinity, which is larger.

Other folks are using integers (1, 2, 3, etc) and rational numbers (1.00000000000…1, 1.00000000000…2, etc), but my way of thinking about this is similar to dimensions, where the fractions of an integer are another dimension applied to those integers, so you have integers (infinite dimension) and the values between the integers (infinite dimension). Unlike simply adding a single dimension though, in this case we’re taking infinite infinities, because between each decimal is an infinity, and the set of decimals is also infinite.

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