I have a background in linguistics (computational) and part of what was mind blowing when my schooling approached the deep dive on some aspects of it was the sh

I have a background in linguistics (computational) and part of what was mind blowing when my schooling approached the deep dive on some aspects of it was the sheer extent to which much of what we put into language is artificially constrained by the limits of any given language being unable to fully express an infinite range of concepts/thoughts/etc… that some things are difficult to put into words because there are no words for every single gradation of a a phenomenon (colors, with their inherent connection to gradients, come to mind). Maybe this seems trivial, I kind of had an intuitive “of course” understanding of it before deep dive work in linguistics, but that’s when it really became abundantly clear how limited we are by lexical entries. All of that is a preamble to say that it seems like the same thing is true of mathematics. No single number system can completely encompass all of mathematical expressions. This post sort of touches on it with the varying methods of expressing something in decimal vs fractional notation. 1/3 cannot be fully expressed (well, expanded) in decimal notation but it is trivial in fractional notation. More esoteric examples exist when entering the realm of hyperreal numbers. It is both amazing and daunting to confront these limits, which may be a product of the limitations of the human mind.(or not, really I don’t know) And maybe I’m just rambling… I don’t have a strong background in number theory… it is all just so beautiful and humbling though.