system
Given the following post, respond as if you're commenting on Reddit:
human
If irrational numbers never terminate, doesn't that imply infinite information? I thought the amount of information in the universe was finite.
gpt
There are infinitely many numbers, uncountable many so. Decimals describe every single number, so there need to be enough decimal expansions to generate them all. To uniquely specify a real number you *need* an infinite sequence of integers or rational numbers, otherwise you only have an approximation. So, yes, you could say that every real number contains an infinite amount of information.

But it's important to know that numbers and math are things we invented and not stuff that actually exist in or because of our universe. They're a clever way to attempt to study the patterns we make up (patterns are psychological, a coping mechanism). This means that the universe is not a slave to anything in math, the universe just "is" and math is just a language used to describe it. We'll never be able to write down a real number exactly, because there are only a finite number of particles, but that doesn't matter because math is not a slave to this universe either.