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 you win a contest and get a literal truckload of Cheerios. The catch is, the Cheerios are all poured into the back of a truck, without individual box packaging. The point is, the number of individual Cheerios in the truck is so huge you can’t count it all.
Imagine you can count up to a million Cheerios by hand. Beyond a million, you just can’t keep track of the number of Cheerios for some reason – you don’t have enough time, you didn’t have enough space in your house, or you don’t know any numbers beyond a million, or no human can possibly count to a larger number than that. The actual reason doesn’t matter, but whatever it is, you can’t count more than a million Cheerios by hand. In fact, the actual limit doesn’t matter either. It can be a million, billion, or quintillion. Let’s call it a flugelbloop. No human can, practically speaking, count more than a flugelbloop of items.
So if someone asks you how many individual Cheerios you have, the best you can say is “more than a flugelbloop”.
Your friend entered the same contest, but won two truckloads of Cheerios. Your friend also has the same limit on the number of Cheerios they can count by hand.
How many Cheerios does your friend have?
Again, the best you can say is “more than a flugelbloop”.
Does your friend have more Cheerios than you? Yes, almost twice as many. Because you can literally take one Cheerio from each of your friend’s two trucks, for each Cheerio from your truck.
But both of you have “more than a flugelbloop” of Cheerios.
How is this possible? Because “more than a flugelbloop” is not a number. It is a concept that means “too many to count”.
In the same way, infinity isn’t a number. It’s a concept that means “too many to count” in a particular mathematical Sense.
You can make a set of things with infinitely many things, in many different ways. In the same way that you took two Cheerios from your friend’s trucks for every one of yours, you can actually prove that some of these sets have more things than other sets, though they all contain infinitely many things.
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