https://www.youtube.com/watch?v=WabHm1QWVCA
I mention him because I would think he sympathizes with those who have concern over the meaning of this kind of notation.
I actually have some sympathies with his contention that real numbers (limit points of infinite series) are somehow a different animal than rational numbers. But it might be easier for me to go there because practically all numbers on computers that we work with are rational, floating point values. On the other hand, it seems like a philosophical distinction in the end because you can fully order them both on a number line.
I guess I shouldn't phrase it as "you can fully order it". :D Zermelo's theorem at that point right?
> but presumably they lie somewhere regardless of my inability to do it on a TM.
Why?
> Zermelo's theorem at that point right?
It is declared by fiat in standard set theory that infinite sets can be well ordered. This is no real mathematical justification. The real justification is social: that it is convenient for mathematicians to not care about the ontology of these nasty infinite objects so long as results are mostly reasonable for objects that mathematicians actually care about. You don't get into too much trouble pretending the reals are nice so long as you don't look too hard.
console.log(0.1 + 0.2)
// 0.30000000000000004
A mathematician might say that this shows that you do not really have accurate floating point values and arithmetic in your computer, but instead something close to it.
Racket starts with arbitrary precision rationals.