mathsandphysics

>The point is that while X (e.g. the real numbers) can be encoded as Y (e.g. Cauchy sequences), this doesn't mean that X is literally Y.

In my opinion, a mathematician does not know what the difference between "being literally" and "being encoded as" is - unless you assume that mathematics should aim to be a formal encoding of some pre-existing 'intrinsic reality', in which case what you're doing is physics and not math.

In physics, the debate is more open: Is the wave function literally the electron? Or is the wave function just an encoding of the electron, which is the intrinsic real thing? Or is the electron the way we humans perceive the wave function, which is the intrinsic real thing?

Anyway this is probably way too theoretical of a debate :)

Real numbers can actually be logically constructed as sets. So yes, Pi is a set.

For example, you can define the set of real numbers as the set of equivalent classes of rational cauchy sequences.

In order words, Pi is a set of rational cauchy sequences that are equivalent (this set is infinite).

In simple (non formal) words: Pi is the set of sequences of rational numbers that get closer and closer to the numerical value of Pi.

>>>> Is 3 an element of pi? If pi truly is a set

Pi being a set doesn't mean that it is a set of real numbers. In fact, that would be illogical (recursive). If Pi is a set, it must be a set of things that are not real numbers. So it is not logical to ask if 3 is an element of Pi. You can ask if 3 is equal to Pi, in which case the answer is no.