Where is i? Is it safe? Is it alright?
this post was submitted on 11 Dec 2023
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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.
You could use ℂ
Quaternions hello?
What about quaternions and octonions and ...
{x | x is a number}
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This image goes so hard
Just like birds, complex numbers aren't real!
Screw you sqrt(-1), you aren't even a real number, you poser!
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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?
What you're probably thinking of is Ordinal numbers.
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".
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Which of the infinities? There are many, many :D
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."
Which of the infinities? There are many, many :D
Oh no! Please don't tell me there are infinity infinities!
Unfortunately yes there are and it's a very big infinity of infinties....
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Wait, they ran out of greek letters and started using Hebrew ones now? When did that happen?
I can't wait to see how much is the number Gimel
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There is nothing "past" infinity, infinity is more a concept than a number, there are however many different kinds of infinity. And for the record, infinity + 1 = infinity, those are completely equal. Infinity + infinity = infinity x 2 = still the same kind of infinity. Infinity times infinity is debatably a different kind of infinity but there are fairly simple ways of showing it can be counted the same.
Essentially the number of numbers between 1 and 2 is the same as the number of numbers between 0 and infinity. They are still infinite.
Hi, I'm a mathematician. My specialty is Algebra, and my research includes work with transfinites. While it's commonly said that infinity "isn't a number" I tend to disagree with this, since it often limits how people think about it. Furthermore, I always find it odd when people offer up alternatives to what infinity is; are numbers never concepts?
Regardless, here's the thing you're actually concretely wrong about: there are provably things bigger than infinity, and they are all bigger infinities. Furthermore, there are multiple kinds of transfinite algebra. Cardinal algebra behaves mostly like how you described, except every transfinite cardinal has a successor (e.g. There are countably many natural numbers and uncountably many complex numbers). Ordinal algebra, on the other hand, works very differently: if ω is the ordinal that corresponds to countable infinity, then ω+1>ω.
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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.
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Doesn't include "i"
i isn't a real number, you imagined it
not a real number
Oh you like math? Name all the sets of sets that don’t include themselves.
0,1,2,3,4,5,6,7,8,9
[0-9]*\.?[0-9]*
edit: ok no empty strings [0-9]+\.?[0-9]*
That regex implies “” is a number
If I had a nickel for every time that happened I'd have "" nickels.
I didn't realize '.' is a number.
\([0-9]+\.[0-9]\)?[0-9]* is more accurate I think.
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Pi
*
i
Fred.
(∀x:Number(x)=T)(Name(x)="Fred")
I name every number Fred.
Which negative infinity or positive infinity includes zero?
Brackets and a comma like that indicate a range, not just a list of 2 values
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.
It's likely just you were taught a different notation. Personally I was taught (x, y) can mean both coordinates x and y or a range from x-y (non inclusive), just depends on context which it is. Brackets like [x,y] I was taught are for inclusive ranges (i.e., x and y are included in the range)
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It's certainly between them somewhere
There is actually zero as well as negative zero for reasons beyond my comprehension
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Where's my imaginary love?
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).
Eldritch numbers.
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