Is infinity bigger than infinity+1?
In: 1
No, partly because infinity is the concept of never ending series of points, not a number we can do arithmatic to.
However, we can define sets to be infinite in size, and then we can do some mathematical things to those sets, but they’re not numbers.
One of the things we can sometimes do to an infinite set is “list” the points on that set. We can take the example of the positive whole numbers. 1, 2, 3… You can list them out in that order.
Now if you want to show if a different infinite set is the same size, all you have to do is match the points from your new set onto the points from this first one. So let’s say you want to do “infinity (meaning the positive whole number list) + 1
Well, we can do that, just add 1 to all of your points.
1+1=2, 2+1=3, 3+1=4…
But now we can take that second list, and match it 1:1 to the first list.
1 matches with 2, 2 matches with 3, 3 matches with 4, and so on. And because there is no last positive whole number, it all matches. And you have proven that the list of positive whole numbers is equal to the positive whole numbers + 1.
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