Real numbers are not "real". (Inspired by Imaginary numbers are not real, an elementary introduction to Clifford Algebra I came across a long time ago).

I find it a bit funny that people tend to think of real numbers as "real" numbers, as opposed to, say, imaginary numbers, which are not only not real, but also not "real" in a way a Realist would use the word. The paper above even takes pride in not using i in calculations. There is also an occasional discussion in philosophy papers and online of the wave function in QM not being "real" because it uses imaginary numbers.

I find it funny because real numbers are no more "real" than any other numbers. Even the set of all integers is not very "real", as basically everything in the Universe is finite, due to the cut-offs at various scales, such as the Planck scale and the age of the Universe, and whenever you try to disregard these cut-offs, things tend to blow up in your face.

One can potentially consider finite integers as the most "real", given that they correspond to discrete objects we can see, count and calculate. The rest are simply useful mathematical abstractions.

One would think that, given that many useful numbers like e and pi are no more "real" than i or infinity, people would get a clue and stop arguing, but no.

<end rant>