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
Imagine Superman is challenged by Batman reach a goal post 10 meters away. Batman says that Superman can only cross this distance by jumping and that Superman can only jump half the remaining distance at a time. So Super jumps once for 5 meters and now there are 5 meters left between Superman and the goal post. Superman jumps again, but this time he can only go 2.5 meters because that is half of the distance, so now Superman has gone 7.5 meters. Another jump and Superman is at 8.75 meters, one more and he is at 9.375 meters. Another way to think about it is that the distance between Superman and the goal is halved every time he jumps. If the distance between Superman and the goal post is 0, he made it.
Now ask yourself the question: If Superman keeps going like this, will he ever reach the goal post? No matter how many times he jumps, there will be some distance left. Think of the biggest number you can and if Superman jumps that many times, there would still be some distance from the goal post.
Eventually, Superman realizes this, and starts using his super speed to jump at an incredibly fast rate. Each jump is a shorter and shorter distance, so Superman can jump faster and faster. Eventually, because he’s Superman, he finally reaches the goal post. But it took him an infinite amount of jumps. Notice how I didn’t say he made infinity jumps? That’s what infinity is: not a number, but a concept. You can say someone made 4 or 5 or 6 things (jumps), but not infinity things (usually described as an infinite amount).
Batman asks to repeat the challenge, but this time Superman can only jump one third of the distance instead of one half. It’s definitely slower than before, but Superman again speeds up and finally reaches the goal post.
Now Batman asks the question: “Which goal post took more jumps to reach?” Both took an infinite amount of jumps (Specifically not “infinity jumps”), but the one-third challenge definitely took more. Thus, one set of an infinite amount of something was more than another.
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