>>12831989>i could give like 4 or 5 definitions of pi right off the top of my headGo on then.
>>hurr durr not rigorous or logical enoughThere's no such thing as "not rigorous enough". It's either rigorous or not. None of the "definitions" of pi are rigorous at all.
>even though everyone who actually has to use pi to compute practical quantities seems to be without issue. Yeah, that's the whole point behind calling it a metanumber. Nobody's quite sure what it is, it seems to be some connected web of nebulous concepts, but whatever it is, it's useful and in some (but not all) ways behaves like actual numbers. That's why it's a metanumber.
>>128319901<1.0000...1...2<2.
>>12831998Of course a circle has a circumference and radius. You can measure it with a meter tape. The ratio of the circumference you measure and the diameter will come out to roughly 3.14. Sometimes more, sometimes less.
However, if you want to talk about idealized circles, things get much more complicated. Before you do that, you first need to define what you mean by a circle, circumference and radius.
>>12832006>There are thousands of geometric and algorithmic explanationsGive one. All of the explanations I've seen have been nonrigorous and handwavy. Do you have an explanation/definition of pi that you think makes sense? If so, please share it with us.
>If that's a decimal representation, and the ellipses stand for an arbitrarily long, finite number of elided digitsNo, it's a decimal expansion where in the first "..." you should substitute infinitely many 3's, and in the second ".." you should substitute infinitely many 2's.
This is supposed to illustrate that just because you can write it down, compare it with actual numbers, and because you think it kinda makes sense, doesn't make it a number.
0.03333...22..55 is not a number until I actually give a proper rigorous definition of what I mean by it. Appealing to vague imprecise notions of substituting infinite digit strings won't do.
