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
You are getting such bad answers here that I feel compelled to write something.
Lets imagine you have a big pile of marbles and so does another guy. You want to see who has more marbles. Obviously you can just count yours, and he counts his, and you compare the results. But here is the catch: The other guy only speaks only French (and you don’t). So if you try this then neither of you will understand what the number was that the other person reached.
Here is a better idea. Instead of counting marbles, you iteratively roll a marble out of your pile. He does the same. You continue until one of you runs out of marbles. Whoever has marbles left at the end is the one who has more marbles.
The second method of comparing sizes still makes sense with infinite sets so this is how mathematicians talk about the “size” of a set (we use the word cardinality). Of course you might simply guess that when comparing infinite sets using the second method, both piles will always run out of marbles at the same time. It turns out that this isn’t the case. The most famous example is the set of reals and the set of naturals. In this example, the naturals run out of marbles before the reals. Hence, we say that the reals are a “larger” infinite set than the naturals.
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