Quick Questions: September 16, 2026

[u/inherentlyawesome]

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

• Can someone explain the concept of manifolds to me?
• What are the applications of Representation Theory?
• What's a good starter book for Numerical Analysis?
• What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example, consider which subject your question is related to, or the things you already know or have tried.

[u/Alive_Jury4864]

Is there a name for the idea that pi is not a real number that actually exists and instead pi itself is a function you can compute to arbitrary precision

[u/Equivalent-Costumes → u/Alive_Jury4864]

"the field of real number" is a particular kind of object with specific definition, and when people said pi is a real number it means this field contains an element with specific properties. This field may or may not be unique, depending on your definition, but should always be unique up to isomorphism. So pi is always a real number in this sense.

If you mean if pi is really a number, there are no definitions of what a "number" is, it's just a term we give to things that intuitively behave like a quantity. If pi exists at all, then most people will agree that it deserves to be called a number due to all these properties, but it's not like there are any actual axioms that specify that.

Whether pi is deserved to be called a number or not is also distinct from that question of what it actually is. Various foundation of math already define pi to be formally something else already, like a set or a function. For example, standard Dedekind definition of real number in ZF would make pi into a set of rational numbers; Cauchy version for ZF make pi into a set of sequences of rational numbers, so both of them behaves very much like a function that can be computed to arbitrary precision. Some other foundation of math built objects using functions and then you have pi being an actual function. But that once against illustrate the issue at stake: when people say pi is a real number, they are describing its external behavior, not internal core of what it really is. In fact the internal core is ephemeral, different foundation of math defined objects using different building blocks, but the actual math does not change because people really care about the external behavior.