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**What does "finite" mean in mathematical terms?**

I was reading a discussion on here about whether or not Pi is infinite. It seems intuitive to me that it's not, but I'm having trouble grasping the idea that it (or any other number) is finite.

From what I understand, if something is finite, it means it is limited or bounded. By that definition, how can a number be finite? What is it "bounded" by? Itself?

Unless my understanding is wrong, and finite just means "not infinite". Is this the correct interpretation, or is there another one?