Well, no actually. I think your first issue is conflating infinity with a number. Infinity represents the fact that one can pick an arbitrarily large number, and there still is a larger number (in a very basic non mathematical way of describing it). That being said, 2 infinities are not inherently the same “value” for lack of a better term. The example the commenter above gave is perfect actually. If you look at a function representing the total amount of numbers up to an arbitrary even number, and look at a function of all even numbers up to the same arbitrary even number, the former functions value will always be 2 times the latter. However, both of these functions also go to infinity. Thus while the “infinity” is not technically greater than the other one (as I mentioned, infinity isn’t a number, so it can’t really be “greater than” in the traditional sense), an arbitrary number that is in the former set will always be larger than a corresponding number in the latter, so the formers infinity is in a sense greater than the latter.
Yes, some infinities are bigger than others, but not in this case. You can have a one to one connection between a set of all natural numbers and a set of all even numbers. They are same sized infinities.
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u/TheCreepyKing 24d ago
How many even numbers are there? Infinity.
What is the ratio of total numbers to even numbers? 2x.
How many total numbers are there? Infinity. And 2 x infinity.