What does it even mean for a number to exist? In math we are happy if the things we talk about are well defined. Numbers are just mathematical objects which sa

What does it even mean for a number to exist? In math we are happy if the things we talk about are well defined. Numbers are just mathematical objects which satisfy a few interesting properties that lead to very rich structures we can study. Some of those structures map onto concepts in nature, which makes them actually useful. Instead of real and imaginary or complex we could have chosen entitirely different adjectives. They're completely arbitrary. They don't matter.