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
So many wrong answers here…
The simple truth is, two sets are the same size if we can have a one-to-one correspondence between their elements.
All “fours” are the same size because you can do that. Four cats vs four tennis balls are the same size because you can pair them up.
You can do that with infinite sets too. There is the same amount of number 1, 2, 3, … and multiples of five because you can pair them up like 1 with 5, 2 with 10, 3 with 15 etc.
But consider the set of all numbers between 0 and 2, including the irrationals. Turns out you cannot produce a correspondence between those numbers and 1, 2, 3, … Try as you will, there will always be numbers not appearing in your correspondence. This can be proven, and the proof us fairly simple.
In other words those two sets though both infinite don’t have the same size. And moreover there’s not only two different infinite sizes. For every infinite size you can find one even larger.
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