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
The different sizes come from countability and uncountability. The counting numbers are the natural numbers 0,1,2,… We can prove that all integers, all coordinates, all rational numbers and all rational complex numbers are the same size as the naturals. We call that countable.
However if we consider infinite decimal expansions, we get an issue where with the Cantor diagonalization argument you can’t list them all. So you can’t match a natural number with them, they’re not the same size. There are more size differences between uncountable sets too because you cannot create an injective or surjective function between the power set of a set and the set.
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