system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Could we find pi as a rational number if we had a different number system?
gpt
I think people are missing the point of the question. It's not "can you write pi in such a way that it terminates," it's "can pi be a rational number." Those are two different things.

Irrationality is not defined as "the number doesn't terminate." That's a property that irrational numbers have when you write numbers in an integer base, but it's not what makes a number irrational. There are plenty (an infinite number) of rational numbers that don't terminate. An irrational number is a number that cannot be expressed as a ratio of two integers (whole numbers).

Writing pi in base pi makes it "look like" a rational number, but it doesn't have the same properties as one. It's still not a ratio of two integers: the set of integers does not change when you use a different number base.