this post was submitted on 11 Sep 2025
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Perry Bible Fellowship
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This is a community dedicated to the webcomic known as the Perry Bible Fellowship, created by Nicholas Gurewitch.
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...? I believe I said the set of hyperreal numbers, which would contain the real numbers cross joined with the set of infinites and infinitesimals. Technically, the infinity that bounds the natural numbers would be any of those infinites. I can't really point to one specific infinity.
Infinity wouldn't be in the set of natural, rational, real, or even complex numbers. It acts as a boundary for all of those sets of numbers, but you could have a set that also includes infinity, in addition to those sets, making them the extended number set.
However, I want to point out an issue with what you said about those being different infinities... That isn't strictly true. Natural numbers, rational numbers, and powers of ten are the same level of infinite. Crazy as it is to imagine, the sets can be functionally mapped to each other. They have the same infinite of elements to them. It isn't until you add in those irrational numbers that the level of infinite increases. There is a higher order of infinite more numbers in the irrational numbers than in the rational numbers, so that infinite IS bigger.
โตโ, the infinity that represents the cardinality of natural numbers, would not be "any infinity" in the set of hyperreal numbers. You have a fundamental misunderstanding of the concept of infinitea if you cannot point to a specific number that "bounds the natural numbers" because that number is โตโ and can be pointed to. It is the only countable infinity. Bring in irrationals and now it is uncountable, because there are an infinite number of numbers between 1 and 2. You can never reach 2 if you counted every number between 1 and 2. The cardinality of irrational numbers is โต1, a distinctly different and larger infinity than โตโ.
Sets like naturals and rationals may have the same cardinality, but they are not functionally the same. Cardinality is just one attribute they share. The powers of 10 cannot be analytically continued to -1/12 like the natural numbers can. Therefore they are functionally different.
Yes, obviously there are different ordinalities to infinites, but for the express purpose of this comic, the particular infinity does not functionally change the comic. The infinity that bounds the real numbers is technically the one that matters, which you are suggesting is somehow different depending on the collection of numbers used to calculate it, which it doesn't. The collection of powers of tens is the exact same as the collection of natural numbers, at infinite scale. It is not some power more, or different. The Euler zeta function doesn't work like that.
Also, there are also an infinite amount of rational numbers between any two rational numbers, even without irrational numbers. The ordinality of the infinite doesn't matter about that, but the ordinality of irrational numbers between them is bigger.