STEM
It’s difficult to comprehend infinity. It’s limitless and boundless, and utterly incomprehensible. The question on whether there is anything greater than infinity has two answers, yes and no, and confusingly both are very much true. Infinity is the largest number as it is, by Is There Anything Bigger Than Infinity? ANNA GRAHAM
both sets are the same size even though you would initially assume the second set has one less number. With sets that go up to infinity, no matter what number you start on there will always be a number in the other set to match to. Visually we can see that when you write out both sets you can always draw a line to match up a number from each set without any overlap. This will go on forever as there is no conceivable end to either sets and so there will always be a number one greater than the previous.
definition, endless. However, can it be said that all infinities are the same size? Before we look at that rather confusing question, we must look at the qualities of the number infinity. First, we must understand that infinity doesn’t work like any other number we are used to using. If you add one to infinity the answer is still infinity. If you multiply infinity by any number (even by infinity itself) the answer is infinity. This is because no matter what, there is still a one-to-one correlation. To explain one-to-one correlation simply, imagine you have a set of {1,2,3,4….} all the way to infinity, and {2,3,4,5….} all the way to infinity. A one-to-one correlation is saying that each number in the set can match up to a number in the other set. In the example set I’ve given,
1, 2, 3, 4, 5, 6, 7, 8,……. ∞
2, 3, 4, 5, 6, 7, 8, 9,……. ∞
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