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
First letʼs try to define, what counting means. To count how much stuff is in a set you assign elements in the set to elements in another set. If two sets can be connected this way, that every element has exactly ine pair, we say that they have the same number of elements. If you can assign every element a number between 1 and 4 using every number only once, you have 4 elements. Every set that has 4 elements has the same number of elements.
What Cantor has proven, however is that you canʼt do this with natural and real numbers. No matter what system you use to assign real numbers to natural numbers, there would always be a real number that have no natural correspondent. Therefore these sets have different number of elements.
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