Last time I saw this kind of challenge it was on reddit and I just replied with ℝ, but people brought up that this leaves out complex numbers. I'll now contend, however, that any number not included in that isn't real.
Aren't there numbers past (plus/minus) infinity? Last I hear there's some omega stuff (for denoting numbers "past infinity") and it's not even the usual alpha-beta-omega flavour.
Come to think of it, is there even a notation for "the last possible number" in math? aka something that you just can't tack "+1" at the end of to make a new number?
As for your second question, I don't think any "last number" could exist unless we explicitly declared one. And even then... I'm not sure what utility there would be in declaring a "last number".
The smallest infinity is the size of the natural numbers. That infinty, Aleph zero, is smaller than the infinity of the real numbers, Aleph one. "etc."
IIRC Depends if you talk about cardinal or ordinal numbers.
What I remember:
In cardinal numbers (the normal numbers we think of, which denote quantity, etc.) have their maximum in infinity.
But in ordinal numbers (which denote order - first, second, etc.) Can go past infinity - the first after infinity is omega. Then omega +1. And then some bigger stuff, which I don't remember much, like aleph 0 and more.
So wait, you can't have numbers larger than infinity, but you can order them "past infinity"? I'm trying to wrap my head around the concept, and the clearest thing I can get at the moment is that the "infinity+1"th number is infinity... would that be right?
No cardinal and ordinal numbers continue past the "first" infinity in modern math. I.e. The cardinal number denoting the cardinality of the natural numbers (aleph_0) is smaller than the one of the reals.
Edit: In modern systems aleph_0 = omega btw. Omega denotes ordinal and aleph denotes cardinals.
After reading how this thread is going I'm half expecting this to be a Kurzgesagt video or something equally "cutesy existential dread" inducing lol. Let's see what do I find!
But those are parentheses, are they not? I was taught intervals using square brackets and semicolon. While parentheses are used for coordinates and tuples. The square brackets indicates inclusion of the boundary number.
Ie. the statement "2
Update: apparently either lemmy or my app (boost) wasn't that excited for my less than signs, and just skipped the rest of the comment. And here I had spent time copying both "less than or equal to" and infinity signs, since my keyboard doesn't seem to have them... For the time being pls disregard the comment above, while I figure out how to write math on lemmy.
Everyone is mentioning the imaginary (and, presumably complex) number domains, but not quaterions and other higher dimensional number sets.
I'm going with defining a describeable number as any number that, given any finite period of time and any finite amount of resources, could be uniquely described to another entity with the ability to read and understand the language it is being described in, then saying all numbers are either describeable numbers (Despite the fact that these are almost laughably uncommon in the scheme of all numbers, I have diligently prepared an example: "2"), or indescribeable numbers (so much more common, and yet I can't give even a single example).