I don't think the word "invented" is much better an analogy for real numbers than "position" is for "where" the Mandelbrot Set is. This goes beyond what is str

I don't think the word "invented" is much better an analogy for real numbers than "position" is for "where" the Mandelbrot Set is. This goes beyond what is strictly math, but I don't think it's reasonable to say that properties of the real numbers (say, roots, pi, e, and so forth) are invented. In some sense they seem like the simplest thing that fits a few properties (and not that many). Similarly with Euclidean Geometry, and the natural numbers (with primes and their structure, etc.) I really actually think something akin to Occam's Razor applies in math! You can of course tweak your starting points and get really interesting things too, say non-standard analysis or non-Euclidean geometries. And you can derive (I would say "discover") some rich and surprising properties and patterns in them. But I don't think any of these things are accidental. The real numbers (and pi, e, etc) would surely be "invented" in the same (modulo shifts in convention) ways by other advanced civilizations, I think. Could you imagine this not being so? This is also extra-mathematical, and I admit this may be hooey, but I believe (as a non-mathematician) that math gives hints at large patterns and tells you when things fit well or are funny. Like, I can argue whether Pi or 2*Pi is the more "natural" constant, and it's not a discussion completely devoid of content! Also, I think math tells me something is funny about 0^0 (because of the limit 0^x) but that 1 is the more natural fit. I realize this puts me quite firmly into the category of people being belittled here!