Nope, you fell for the classic sibling blunder:
What about INFINITY PLUS ONE!?
gatekeeping
Submitted 11 months ago by fossilesque@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/e07e4ad2-77e6-40b2-9d77-51c8422ed83b.jpeg
Comments
ivanafterall@kbin.social 11 months ago
Yondoza@sh.itjust.works 11 months ago
Infinity! Infinity -1, also infinity! Well what about infinity * infinity? Believe it or not, infinity! ♾️
rockerface@lemm.ee 11 months ago
Infinity gangsta when aleph null walks in
Kase@lemmy.world 11 months ago
Oh yeah? What’s infinity divided by zero?
CarbonIceDragon@pawb.social 11 months ago
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.
fossilesque@mander.xyz 11 months ago
zzx@lemmy.world 11 months ago
This image goes so hard
BigDanishGuy@sh.itjust.works 11 months ago
Just like birds, complex numbers aren’t real!
Screw you sqrt(-1), you aren’t even a real number, you poser!
vsh@lemm.ee 11 months ago
I prefer $
FooBarrington@lemmy.world 11 months ago
Complex numbers? That sounds imaginary.
veniasilente@lemm.ee 11 months ago
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?
kerrigan778@lemmy.world 11 months ago
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.
Leate_Wonceslace@lemmy.dbzer0.com 11 months ago
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 all are bigger infinities. Furthermore, there are multiple kinds of transfinite algebra. Cardinal algebra behaves mostly like how you described, except every transfinite cardinal has 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.
CompassRed@discuss.tchncs.de 11 months ago
You have the spirit of things right, but the details are far more interesting than you might expect.
For example, there are numbers past infinity. The best way (imo) to interpret the symbol ∞ is as the gap in the surreal numbers that separates all infinite surreal numbers from all finite surreal numbers. If we use this definition of ∞, then every infinite ordinal number is greater than ∞. For example, every infinite surreal number is greater than ∞ by the definition of ∞. Furthermore, ω > ∞, where ω is the first infinite ordinal number. This ordering is derived from the imbedding of the ordinal numbers within the surreal numbers.
Additionally, as a classical ordinal number, ω doesn’t behave the way you’d expect it to. For example, we have that 1+ω=ω, but ω+1>ω. This of course implies that 1+ω≠ω+1, which isn’t how finite numbers behave, but it isn’t a contradiction - it’s an observation that addition of classical ordinals isn’t always commutative. It can be made commutative by redefining the sum of two ordinals, a and b, to be the max of a+b and b+a. This definition is required to produce the embedding of the ordinals in the surreal numbers mentioned above (there is a similar adjustment to the definition of ordinal multiplication that is also required).
Note that infinite cardinal numbers do behave the way you expect. The smallest infinite cardinal number, ℵ₀, has the property that ℵ₀+1=ℵ₀=1+ℵ₀. For completeness sake, returning to the realm of surreal numbers, addition behaves differently than both the cardinal numbers and the ordinal numbers. As a surreal number, we have ω+1=1+ω>ω, which is the familiar way that finite numbers behave.
What’s interesting about the convention of using ∞ to represent the gap between finite and infinite surreal numbers is that it renders expressions like ∞+1, 2∞, and ∞² completely meaningless as ∞ isn’t itself a surreal number - it’s a gap. I think this is a good convention since we have seen that the meaning of an addition involving infinite numbers depends on what type of infinity is under consideration. It also lends truth to the statement, “∞ is not a number - it is a concept,” while simultaneously allowing us to make true expressions involving ∞ such as ω>∞. Lastly, it also meshes well with the standard notation of taking limits at infinity.
KmlSlmk64@lemmy.world 11 months ago
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.
weker01@feddit.de 11 months ago
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.
veniasilente@lemm.ee 11 months ago
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?
Leate_Wonceslace@lemmy.dbzer0.com 11 months ago
Hi! I’m a mathematician, and if you want to know more about infinity, I recommend this video: youtu.be/23I5GS4JiDg
veniasilente@lemm.ee 11 months ago
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!
jflorez@sh.itjust.works 11 months ago
There is nothing past infinity on the real number line. Then there is the imaginary line that gives you an infinity for the complex numbers
768@sh.itjust.works 11 months ago
I cast set theory?
Adalast@lemmy.world 11 months ago
I was thinking the same thing.
768@sh.itjust.works 11 months ago
Thanks.
CJOtheReal@ani.social 11 months ago
Doesn’t include “i”
Godort@lemm.ee 11 months ago
i isn’t a real number, you imagined it
BolexForSoup@kbin.social 11 months ago
From gatekeeping to gaslighting in 2 comments. Not bad!
callyral@pawb.social 11 months ago
not a real number
hansl@lemmy.world 11 months ago
Oh you like math? Name all the sets of sets that don’t include themselves.
zzx@lemmy.world 11 months ago
Russell is that you? Please stop breaking my formal systems
NegativeInf@lemmy.world 11 months ago
Here’s a thousand page proof defining all the logical underpinning required to prove that 1 does indeed equal 1.
Stupidmanager@lemmy.world 11 months ago
0,1,2,3,4,5,6,7,8,9
wafflez@lemmy.world 11 months ago
Zero’s not real
Ofosho@hexbear.net 11 months ago
I thought it was ‘R’, for the set of all real numbers.
SpongyAneurism@lemmy.frozeninferno.xyz 11 months ago
Oh, so complex numbers are not numbers now?!
Bizarroland@kbin.social 11 months ago
You also have to remember to put the +C at the end
blanketswithsmallpox@lemmy.world 11 months ago
Which negative infinity or positive infinity includes zero?
rbesfe@lemmy.ca 11 months ago
Brackets and a comma like that indicate a range, not just a list of 2 values
BigDanishGuy@sh.itjust.works 11 months ago
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
wanderer@lemmy.world 11 months ago
wetnoodle@sopuli.xyz 11 months ago
It’s certainly between them somewhere
bfg9k@lemmy.world 11 months ago
There is actually zero as well as negative zero for reasons beyond my comprehension
blanketswithsmallpox@lemmy.world 11 months ago
That was the root of what I was getting at, thanks lol.
callyral@pawb.social 11 months ago
*
Leate_Wonceslace@lemmy.dbzer0.com 11 months ago
Fred.
(∀x:Number(x)=T)(Name(x)=“Fred”)
I name every number Fred.
ColdWater@lemmy.ca 11 months ago
Didn’t it 0,1,2,3,4,5,6,7,8,9?
starman2112@sh.itjust.works 11 months ago
That’s just all the Arabic numerals
NorthWestWind@lemmy.world 11 months ago
Where’s my imaginary love?
prime_number_314159@lemmy.world 11 months ago
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).
NegativeInf@lemmy.world 11 months ago
Eldritch numbers.
ILikeBoobies@lemmy.ca 11 months ago
Depends on the bit limit
Mr_Fish@lemmy.world 11 months ago
Where is i? Is it safe? Is it alright?
runswithjedi@lemmy.world 11 months ago
Don’t worry you’re just imagining it.
kpw@kbin.social 11 months ago
Please stop talking about your imaginary girlfriend, it's embarrassing honestly.
veniasilente@lemm.ee 11 months ago
It seems in your equations, you conjugated it.
WhiskyTangoFoxtrot@lemmy.world 11 months ago
i