On the first use of decimal points: https://www.npr.org/2024/02/24/1233702474/the-decimal-point-was-in-use-150-years-before-previously-thought-research-shows
My discomfort with the decimal / base 10 system is...it's too popular. For too many people, it's our only conceptual way of understanding real numbers.
I remember taking real analysis as an undergrad, and not really getting it. It took me years until I could pry my brain away from conceiving of real numbers as something different from their representation as decimal expansions.
For example, people say π "is" 3.14159...and that it "goes on forever". Well, no: the sequence of symbols that starts with 3.14159 is one way of *representing* π, and it's only that representation that goes on forever; as a number, π is, well: π.
If I ever get the chance to teach undergrad real analysis, I want to focus the course on showing students just what the real numbers (and functions thereof) *are*, and how unspeakably strange …
