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
Some infinite sets of numbers have a clear starting point and a clear way to progress through them, like the natural numbers (1,2,3,…). It’s very easy to count the numbers of this set, and therefore its size is said to be countably infinite.
Some infinite sets of numbers do not have a clear starting point and do not have a clear way to progress through them, like the real numbers. Take all the decimal numbers between 0 and 1. What number follows 0? 0.00000000…1? Not really. It’s impossible to count the numbers of this set, and therefore its size is said to be uncountably infinite.
One can use clever tricks, like [Cantor’s Diagonal Argument](https://en.m.wikipedia.org/wiki/Cantor’s_diagonal_argument ), to show that there are more real numbers than natural numbers, which is why we say uncountable infinity is larger than countable infinity.
Edit: The mathematically precise way to describe it is not to compare the size of “infinities”, but rather to compare the size of infinite sets. A mathematician would say that the size of the set of real numbers is larger than the size of the set of natural numbers.
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