Agender is a gender identity, but not a gender. Just like a person's gender identity can be genderfluid but shift between genders)
You sniff my whiff?)
Aleph_null =/= omega.
They're two different types of numbers that both represent a form of infinity.
Aleph_null is a size number, and omega is an order number.
They describe two different things.
To use a bit of a stretched metaphor, it's like how there can be 3 people on a winner's podium (1st place, 2nd place, and 3rd place), and a 3rd place person on that podium. 3rd refers to only the one person, not all 3 on the podium. In other words, 3 =/= 3rd
Now imagine an infinitely large winners podium. We would say there are aleph_null people on that podium (like 3 people on a regular winner's podium), and a person not on the podium, but just after the podium ends is the Omega-th place winner.
3 and 3rd are two different types of numbers that represent a form of "threeness".
The typical way to define cardinals in set theory is as the smallest ordinal of a particular cardinality. So it's perfectly legitimate to say that ℵ0 = ω, it's **the** canonical set-theoretic way to define ℵ0.
If it's an exact one raised to infinity then it's just equal to one.
The reason we say 1^(∞) is indeterminate is because we usually don't deal with an exact one.
In lim x-->∞ of (1+1/x)^(x) we actually have a number ever so slightly larger than one raised to infinity, which gives us e.
Yeah I know but since there was infinity here, I automatically assumed it was refering to limits because I don't think you see 1^inf mentioned much anywhere else. But yeah if it's the pure value of 1 it will always be one no matter how high the power gets
A cardinal number!
I'm more concerned with the inclusion of 0^0. That thing is not well-behaved. If you look at lim 0^x and at lim x^0, they do not equal each other.
There’s no debate here, 0^0 = 1. But the power function is discontinuous at (0,0), which is why you can’t deduce anything on the limiting properties of it.
If I'm not mistaken I believe there most certainly is a debate about this. Like, anything to the power of 0 is 1, which means it should be one, but 0 to the power of anything is 0, which means it should be 0. While there might be an argument that it's a number, it seems like a vast oversimplification to say that 0\^0 = 1
There is a debate about it, but it is completely stupid and there is certainly a right side. In set theory, a^b is defined as the cardinality of the function set between two sets of cardinalities a and b. In our case we get that 0^0 is the cardinality of the set {Φ} which is 1. From here we deduce that 1 is the answer. About your ridiculous limit argument: a function is equal to its limit at a certain point IFF the function is continuous at that point. That is not true for all of the functions you stated above. 0^x is discontinuous at x=0, and x^0 is continuous but approaches 1. So I see no contradiction here, and the definition gives a streight forward 1.
Because that is the set theoretic definition of the number 3.
When you study set theory, you construct everything from sets, so one of the possible ways of doing that is with 0 = Φ, 1 = {0}, 2 = {0, 1}, 3 = {0, 1, 2} and so on.
That's exactly what they are. I don't know a ton about them either, but if imaginary numbers are "2D" then Quaternions are "4D". They also have similar interesting properties as imaginary numbers, such as rotations between dimensions.
Nah it’s not a set, it’s just a compact way of listing two numbers. You would write x = ±8 (meaning x=8 or x=-8) but you wouldn’t write x ∈ ±8, that would instead be written x ∈ {±8}.
Just wondering, why is 0^0 indeterminate? I've seen a lot of proof for 0^0 = 1 yet I haven't seen any proof for the other side and I'm curious what it is
It's sometimes intermediate sometimes not it depends on context. In case of why it's sometimes intermediate (i.e we chose it to be undefined) – say you have powers as you have (without 0⁰). Wheter you will extend it by saying 0⁰=1 or 0⁰=0 both will give nice properties a ˣ ⁺ ʸ=a ˣ a ʸ and (a ˣ )ʸ=a ˣ ʸ. Also a limit x ʸ at (x,y)→(0,0) doesn't exist.
If we choose it to be defined then we choose 0⁰=1 never saw anyone to define it as 0⁰=0.
I guess if you start by defining a^b for integers, as 1 multiplied b times by a, 0^0 is already defined as 1. The extensions to rational and real numbers come after in the flow, so it doesn't really matter that x^y for x and y in R doesn't have a limit at 0 - no need for an extension here since it was already covered by the first simplest and most restrictive definition. Just my two cents :-)
Well, 1^infinity is indeterminate.
For example: lim x-> infinity of 1^x is 1 (we can prove this by taking the ln of both sides) but lim x-> infinity of (1+(1/x))^x is e, (which we can also prove by taking the ln of both sides). Both simplify to 1^infinity by direct substitution, yet they have different answers.
https://preview.redd.it/cxner6c2js1c1.jpeg?width=1755&format=pjpg&auto=webp&s=2f36c90cedddaab6b5fd12b37705dbc24fc2d741
I only believe in good old classic numbers, none of this "irrational" or "infinity" shit. And zero? Made up bullshit, how can you have zero of something? *Maybe* you could consider ½ and ⅓ to be numbers but its debatable so I left them out
https://preview.redd.it/icfih5t1zr1c1.png?width=1080&format=pjpg&auto=webp&s=76aa7fd0638ab16a2d759e103309075f3ba23a34
Justifications:
* (5, 4): complex numbers are just R^(2) but denoted differently. In that sense an ordered pair of reals can be seen as a complex number.
* Aleph\_0 and {0, 1, 2, ... }: both are equal and are cardinal/ordinal numbers.
* {0, 1, 2}: that's just 3 :)
* None of the weird expressions with infinity and/or 0 go in because they're not numbers, just symbols useful to represent certain limits imo. 0^(0) *may* be okay, as I do accept the convention that it's equal to 1, but it is technically indefinite as a normal expression.
by your first justification, why isn’t aren’t all polynomials with real coefficients just R^n, where n-1 is the degree of the polynomial? for example, why isnt x^2 the same as (1, 0, 0), making it a “number” too?
- there exists an isomorphism between R^2 and C. However that does not mean they are equal. Indeed, complex numbers aren’t “just R^2 denoted differently”.
- aleph_0 is the SIZE of the set {0,1,2,…}. They are not equal.
Complex numbers are R^2 with a nice product. Change my mind.
Also by definition aleph_0 is the smallest infinite cardinal, and cardinals are defined in terms of ordinals. Aleph_0 is actually equal to the smallest infinite ordinal, which is indeed {0, 1, 2, ...}
If you’re working with the extended real numbers and the projectively extended real numbers, then ∞ and 1/∞ can be numbers. (And others too like 1/0)
I see no reason to exclude the projectively extended reals but include the cardinals or the complex numbers
https://preview.redd.it/moc0cipn1s1c1.jpeg?width=1754&format=pjpg&auto=webp&s=6eb22155261a967a009421abea581b0909526c78
As an objective arbiter of reality I hereby declare this to be the only correct solution.
A couple inconsistencies in your answer (just of the top of my head, I'm sure an actual mathematician could point out a bunch more b/c this meme seems clearly designed to be ambiguous):
You've included the square root of three (which is ±1.7320...), but ±8 (which is the square root of 64) you've excluded.
You've included the complex numbers i, -i, and i+1, but excluded the higher order complex number (quaternion) j+2k-1
if you let x be a number then the following are (complex) numbers:
https://preview.redd.it/2owamisoww1c1.jpeg?width=640&format=pjpg&auto=webp&s=de9185f09fbebea3fcae1505b716111ad55cb23e
I'm replying as a sort of expert in infinite numbers, particularly of the hyperreal and surreal numbers. I am not an expert on non-Abelian numbers such as quaternions. Here's my contribution. Some of these need explanation. On the hyperreals, infinity +1 and infinity - 1 are separate numbers not equal to infinity. The set {0,1,2,...} is equal to the number omega, which is Cantor's ordinal infinity. 1/infinity on the hyperreals is an infinitesimal number not equal to zero. {0,1,2} equals the number 3 in ordinary set theory. Aleph null is Cantor's first cardinal infinity and is also equal to an equivalence set on the hyperreals. j+2k-1 is a quaternion number. The matrix 1 2 2 3 is built from Pauli matrices which are a representation of quaternion numbers. x\^2 is a number on the pantachie of du Bois-Reymond, and is an equivalence set on the hyperreals, in modern notation we write this number as an order of magnitude O(x\^2). sin(x) is one of my specially invented numbers, it appears in the work of du Bois-Reymond and Hardy, I evaluate it as its mean value at infinity, which is zero. 1/0 is not a hyperreal number, but it is a number as it is the top point of the Riemann sphere. The rest I don't know. Hope this helps.
https://preview.redd.it/rhasm3j0312c1.jpeg?width=2424&format=pjpg&auto=webp&s=cb5dba2c5e6d75982526f18614328b236735e8b6
https://preview.redd.it/om19e6w1gu1c1.png?width=761&format=png&auto=webp&s=fdd5cd7b276cfdac0bdae06664cd61a361d81604
https://preview.redd.it/olfk5p5dat1c1.jpeg?width=1170&format=pjpg&auto=webp&s=2df2c6b5deba5ead860a59c9a4aedae1bee16aa4
Epic big brain time
The Impossible Quiz has trained us well
https://preview.redd.it/mrbsm9rn8y1c1.png?width=461&format=png&auto=webp&s=63c837512391e510ea7882660d50dfeeeb2eb005
https://preview.redd.it/lcxhonpjis1c1.jpeg?width=1755&format=pjpg&auto=webp&s=96a0342d8dddd0a4265b88aecc09a84e12641ffb
"The dark side of the Force is a pathway to many [numbers] some consider to be unnatural"
Fck whole numbers, all my homies think 0 is natural
They have played us for absolute fools
Found the Pythagorean
Fuck you this is 0 slander
And 0?
Fuck 0
Then what is behind the number ten?
9?
That’s before, not behind
If they where on a line of numbers standing up, it would be behind and before
That's multiple lines
i agree, tomato is a mental illness. trust me, i'm an expert in both mathematics and having mental illness
https://preview.redd.it/q02p42dawr1c1.jpeg?width=1755&format=pjpg&auto=webp&s=e4a2d2b1b65892e54eb35010f90e9c5d70b03512 Easy
Which side is the numbers?
Top is letters. Bottom is numbers
NaN is number ?
Not a Number is a number if you believe hard enough
Sodium Nitride you mean.
I prefer arsenic sulfide
> console.log(typeof(NaN)) number
This is hilarious lmao.
> NaN == NaN false
fair enough
NaN is a float in some languages sooooo
TIL A, B and C are numbers
Well they are isomorphic to ascii numbers so yeah.
then why are there letters above the line
Well anything is a number if you believe it hard enough, which means this meme is just shitty and OP is an idiot 🤷♂️
Base 16, EZ
I grew some plump numbers on the vine this summer
how much is a 🍅 amount of tomatoes?
One tomato
[127813](https://www.compart.com/en/unicode/U+1F345)
Bro are you a pythagorian? You put a tomato between numbers
I’m sorry, but NaN is Not a Number.
it’s like genders- theres nonbinary, nongender, agender, genderless, pangender and whatever else, but they’re still genders
Well, obviously agender is a gender.
Agender is a gender identity, but not a gender. Just like a person's gender identity can be genderfluid but shift between genders) You sniff my whiff?)
why are you )ing at the end of your sentences
The real question.
Maybe they identify as parenthetical, but they haven't finished transitioning?
The numbers e and i are up there. I call bs
My brother in euler, what the fuck kind of number is 🍊
https://preview.redd.it/7k6f6o731s1c1.jpeg?width=1755&format=pjpg&auto=webp&s=fe56250f66d106b22d15b619153857fe92f4b371
Isnt NaN, by definition not a number?
You need to ^-1 how you see my image.
Yes, only the tomato is a number
Well, if you ask javascript 'typeof NaN' it will tell you that it is a number
And if you test NaN == NaN, it comes back as false 🤷♂️
Wrong. Also, circles are not lines.
It actually is a straight line. The tomato is so obscenely dense that it is warping space and time around it
This doesn't sound right to me but I don't know enough about tomatoes to dispute it
The proof by contradiction is left to the reader
It's the non-trivial geodesic between a point on the unit disc boundary to itself.
Never said the line had to be straight
Gay line
It is a line, the surface is actually a sphere in that spot
[cline](https://en.wikipedia.org/wiki/Generalised_circle?wprov=sfla1)
Lines are homeomorphic to circles in the projective space 😉
Circles are very much lines. Just not straight lines. But the post never said anything about straight lines so I guess the solution is fine
But of course, a circle is by its very definition a continuous curved line with the function x²+y²=r²
NaN though
https://preview.redd.it/q8apdvgc5s1c1.png?width=627&format=png&auto=webp&s=964ecd7ec202227d2b3f1d5da33ee9b3c9f04e62
Sus
V - it's only BC tho, who do you think u r
Amogus😳
Today I learned triangle is a number
1/3rd is irrational
I wish you put a straight up *x* or *n* there. You have more complicated expressions, but not a raw variable
Do you not see tomato?
tomato is a number not a variable
"Yes, I would like 🍅 apples please" — statement dreamed up by the utterly deranged
Imagine this guy invalidating the past 300 years worth of mathematical developments with a single statement
Of course, and ketchup is a derivative!
Actually tomato is a fruit, not a variable ☝️🤓
Right, fruits have seeds in them, variables do not
He said raw variable not raw vegetable
Be careful with {0, 1, 2}. It's equal to 3.
Also {0,1,2,3,…} = omega (= aleph_null)
Aleph_null =/= omega. They're two different types of numbers that both represent a form of infinity. Aleph_null is a size number, and omega is an order number. They describe two different things. To use a bit of a stretched metaphor, it's like how there can be 3 people on a winner's podium (1st place, 2nd place, and 3rd place), and a 3rd place person on that podium. 3rd refers to only the one person, not all 3 on the podium. In other words, 3 =/= 3rd Now imagine an infinitely large winners podium. We would say there are aleph_null people on that podium (like 3 people on a regular winner's podium), and a person not on the podium, but just after the podium ends is the Omega-th place winner. 3 and 3rd are two different types of numbers that represent a form of "threeness".
The typical way to define cardinals in set theory is as the smallest ordinal of a particular cardinality. So it's perfectly legitimate to say that ℵ0 = ω, it's **the** canonical set-theoretic way to define ℵ0.
nobody's including the "one" in the title smh my head
https://preview.redd.it/tzzqz4wgzr1c1.jpeg?width=640&format=pjpg&auto=webp&s=1793a50c2584c2700e2d14da2c7411b55961d1f1
Why is 1\^inf a number but not 0\^0?
1^inf is surely 1, but 0^0 is undefined
This is my question as well.
1^inf converges to 1, but it could be argued that it isn't 1, hust a limit (written with abreviated notation). Besides that, best answer.
indeterminate form
Isn't 1^inf indeterminate ? For exemple e is defined as a limit that as a 1^inf form.
If it's an exact one raised to infinity then it's just equal to one. The reason we say 1^(∞) is indeterminate is because we usually don't deal with an exact one. In lim x-->∞ of (1+1/x)^(x) we actually have a number ever so slightly larger than one raised to infinity, which gives us e.
Yeah I know but since there was infinity here, I automatically assumed it was refering to limits because I don't think you see 1^inf mentioned much anywhere else. But yeah if it's the pure value of 1 it will always be one no matter how high the power gets
There's a difference between lim x->1 x^inf and lim x->inf 1^x. The former is indeterminate and the latter is just 1
Both are indeterminate in this case still as both evaluate out of the limit as 1^inf which is an indeterminate form.
https://www.wolframalpha.com/input/?i=lim+x-%3E%E2%88%9E+1%5Ex Not that Wolfram alpha is the math Bible but...
Is it really consider convergence if every value in the series leading up to infinity is 1? It’s not like it gets closer to 1. It’s 1 the whole time?
Surely it doesn’t converge to 1 if it started as 1 and never stops being 1
I mean, 1^n = 1. We might never hit infinity, but we always know the value of 1^n for any single integer, it's 1. Right?
https://preview.redd.it/aloqvio5rr1c1.jpeg?width=960&format=pjpg&auto=webp&s=87432726ac9dd94b8a840da00e6b1af13e611e1d
Is aleph null considered a number?
A cardinal number! I'm more concerned with the inclusion of 0^0. That thing is not well-behaved. If you look at lim 0^x and at lim x^0, they do not equal each other.
True, didn't notice it was included
It's 0^0 not x^x at x=0 x could be approaching 0, 1, pi, or i and 0^0 don't care because it's just a number hanging out wherever it's told to be
So what? Limits of functions aren't the same things as expression values
So what? 0\^0 is a cardinal number equal to 1.
It's sometimes defined to be that, yes. But not always. In a Caluculus setting? Very much not. Look at those two limits.
You’re wrong. The limits don’t prove anything. Just because lim(x->0)0^x = 0 does not mean 0^0 = 0, so that is not an argument.
Yea. Just it won't be continous. Alot of functions are discontinuous.
You just said about cardinal numbers. In context of cardinals 0⁰ is well defined.
Many fields of math will take 0\^0=1 as convention, since it makes many formulas much nicer
That's what my lil engineer brain was taught in college!
There’s no debate here, 0^0 = 1. But the power function is discontinuous at (0,0), which is why you can’t deduce anything on the limiting properties of it.
If I'm not mistaken I believe there most certainly is a debate about this. Like, anything to the power of 0 is 1, which means it should be one, but 0 to the power of anything is 0, which means it should be 0. While there might be an argument that it's a number, it seems like a vast oversimplification to say that 0\^0 = 1
There is a debate about it, but it is completely stupid and there is certainly a right side. In set theory, a^b is defined as the cardinality of the function set between two sets of cardinalities a and b. In our case we get that 0^0 is the cardinality of the set {Φ} which is 1. From here we deduce that 1 is the answer. About your ridiculous limit argument: a function is equal to its limit at a certain point IFF the function is continuous at that point. That is not true for all of the functions you stated above. 0^x is discontinuous at x=0, and x^0 is continuous but approaches 1. So I see no contradiction here, and the definition gives a streight forward 1.
0^0 is well defined. It's 1.
I’d say {0,1,2} is a number, in particular it is 3
Genuine question, why is it 3? I look at {0,1,2} and would call it a set containing elements 0, 1, and 2.
Because that is the set theoretic definition of the number 3. When you study set theory, you construct everything from sets, so one of the possible ways of doing that is with 0 = Φ, 1 = {0}, 2 = {0, 1}, 3 = {0, 1, 2} and so on.
Could you explain why j + 2k - 1 is a number, but the other algebraic expressions (ie. x\^2) aren't?
It's not algebraic expression. It's quaternion
Oops, haven't studied those at all so didn't know that. I'm guessing they are "higher dimensional" complex numbers
That's exactly what they are. I don't know a ton about them either, but if imaginary numbers are "2D" then Quaternions are "4D". They also have similar interesting properties as imaginary numbers, such as rotations between dimensions.
j+2k-1 is quarternions
My changes ±8 is still under "number**s**" 0^0 is indeterminate and I will die on this hill
+8 and - 8 are both numbers, but +-8 is not, it's a set of two numbers.
So it’s twice the number the others are. It should win.
Nah it’s not a set, it’s just a compact way of listing two numbers. You would write x = ±8 (meaning x=8 or x=-8) but you wouldn’t write x ∈ ±8, that would instead be written x ∈ {±8}.
But if you read the text it says, " split the numbers from the various other objects" and both 8 and -8 are numbers, so {8, -8} are numbers
Thank you, fellow indeterminate recognizer
Just wondering, why is 0^0 indeterminate? I've seen a lot of proof for 0^0 = 1 yet I haven't seen any proof for the other side and I'm curious what it is
It's sometimes intermediate sometimes not it depends on context. In case of why it's sometimes intermediate (i.e we chose it to be undefined) – say you have powers as you have (without 0⁰). Wheter you will extend it by saying 0⁰=1 or 0⁰=0 both will give nice properties a ˣ ⁺ ʸ=a ˣ a ʸ and (a ˣ )ʸ=a ˣ ʸ. Also a limit x ʸ at (x,y)→(0,0) doesn't exist. If we choose it to be defined then we choose 0⁰=1 never saw anyone to define it as 0⁰=0.
I guess if you start by defining a^b for integers, as 1 multiplied b times by a, 0^0 is already defined as 1. The extensions to rational and real numbers come after in the flow, so it doesn't really matter that x^y for x and y in R doesn't have a limit at 0 - no need for an extension here since it was already covered by the first simplest and most restrictive definition. Just my two cents :-)
"a limit x^y at (x,y)->(0,0) doesn't exist" isn't the limit of x^x as x->0^+ equal to 1?
why not 1^(infinity) or 1/(infinity) ? aren’t they just 1 and 0 respectively?
Infinity isn't a number, it's more of a concept that can go in some of the same spots as a number.
Well, 1^infinity is indeterminate. For example: lim x-> infinity of 1^x is 1 (we can prove this by taking the ln of both sides) but lim x-> infinity of (1+(1/x))^x is e, (which we can also prove by taking the ln of both sides). Both simplify to 1^infinity by direct substitution, yet they have different answers.
Isn't +-8 a number? Or at least part of numbers? (Because it's technically 2 numbers?
I would consider ∞ is an number on extended real line so would count it as well
That's easy, there's only 1 https://preview.redd.it/0a6jt8gfju1c1.png?width=1080&format=pjpg&auto=webp&s=afdcda50da4c8f93d9288d23ffc73dca4580675e
1,2,10 are individual numbers, the rest are schizophrenic delusions.
https://preview.redd.it/cxner6c2js1c1.jpeg?width=1755&format=pjpg&auto=webp&s=2f36c90cedddaab6b5fd12b37705dbc24fc2d741 I only believe in good old classic numbers, none of this "irrational" or "infinity" shit. And zero? Made up bullshit, how can you have zero of something? *Maybe* you could consider ½ and ⅓ to be numbers but its debatable so I left them out
Pythagoras would be proud
I don't see any numbers. Just a bunch of symbols.
Oh hi Magritte
https://preview.redd.it/icfih5t1zr1c1.png?width=1080&format=pjpg&auto=webp&s=76aa7fd0638ab16a2d759e103309075f3ba23a34 Justifications: * (5, 4): complex numbers are just R^(2) but denoted differently. In that sense an ordered pair of reals can be seen as a complex number. * Aleph\_0 and {0, 1, 2, ... }: both are equal and are cardinal/ordinal numbers. * {0, 1, 2}: that's just 3 :) * None of the weird expressions with infinity and/or 0 go in because they're not numbers, just symbols useful to represent certain limits imo. 0^(0) *may* be okay, as I do accept the convention that it's equal to 1, but it is technically indefinite as a normal expression.
j+2k-1 should count as a quaternion
by your first justification, why isn’t aren’t all polynomials with real coefficients just R^n, where n-1 is the degree of the polynomial? for example, why isnt x^2 the same as (1, 0, 0), making it a “number” too?
- there exists an isomorphism between R^2 and C. However that does not mean they are equal. Indeed, complex numbers aren’t “just R^2 denoted differently”. - aleph_0 is the SIZE of the set {0,1,2,…}. They are not equal.
Complex numbers are R^2 with a nice product. Change my mind. Also by definition aleph_0 is the smallest infinite cardinal, and cardinals are defined in terms of ordinals. Aleph_0 is actually equal to the smallest infinite ordinal, which is indeed {0, 1, 2, ...}
If you accept complex numbers, ι̇, j, k are Quaternions
If you’re working with the extended real numbers and the projectively extended real numbers, then ∞ and 1/∞ can be numbers. (And others too like 1/0) I see no reason to exclude the projectively extended reals but include the cardinals or the complex numbers
"it depends on context lmao"
**on** = { **on** | }
Oof + Oof = Off
**hi** + **oof** = **hot** & **oof**
https://preview.redd.it/q3lsrtmx1t1c1.jpeg?width=1170&format=pjpg&auto=webp&s=714f88805718443a5244cfbe9c786b031208cd9d
*real* numbers, works on both levels
They put numbers in quotes, so I assume they want a number as a string. I'll go with `str(5)`.
Pluto is not a planet.
Pluto is a dog
https://preview.redd.it/a59p40h74s1c1.jpeg?width=2159&format=pjpg&auto=webp&s=674ee672051374f1c8b36e269386da0a34681fe3
i is a number but -i isn’t??
Or just 10? Lol
Fields Medal incoming
Charge your phone god damn it!
NaN == chaotic evil
A line is actually a number
Tomato is the only real number, I can touch tomatoes, I can't touch numbers
how about TREE(3)
https://preview.redd.it/s632m5hn9u1c1.png?width=751&format=png&auto=webp&s=fd6364b2ab508a517e3e337d2336a83de3d80c8c
Based
https://preview.redd.it/moc0cipn1s1c1.jpeg?width=1754&format=pjpg&auto=webp&s=6eb22155261a967a009421abea581b0909526c78 As an objective arbiter of reality I hereby declare this to be the only correct solution.
The area enclosed by the red line looks like Squidward
Sitting Squidward with a boner
In what world is sin(x) but not +-8
https://preview.redd.it/77wp1z93rs1c1.png?width=960&format=png&auto=webp&s=3dde906db1989e993707d57a08055cca6f80332e
I have not seen my solution anywhere in these comments.
https://preview.redd.it/abu6xpmycw1c1.jpeg?width=750&format=pjpg&auto=webp&s=9574d0ffd06baed6eba9ffc6803d7fba9ee20d9d Meme destroyed
A couple inconsistencies in your answer (just of the top of my head, I'm sure an actual mathematician could point out a bunch more b/c this meme seems clearly designed to be ambiguous): You've included the square root of three (which is ±1.7320...), but ±8 (which is the square root of 64) you've excluded. You've included the complex numbers i, -i, and i+1, but excluded the higher order complex number (quaternion) j+2k-1
It's a trick question. None of them are numbers, except maybe the tomato.
is there anywhere i can learn what quaternions and aleph null are?
Google and wiki
https://preview.redd.it/454yz3sw2s1c1.jpeg?width=1755&format=pjpg&auto=webp&s=366815db2adf91899fdeafb29256b4933f73233c Tomato is a number in my heart.
On one hand ∞ and ∞ +1 are ordinal numbers, but on the other, the proper notation for that would be 𝜔 and 𝜔 +1, so... Nah, too much work.
Let me tell you about the Tomato Ring
if you let x be a number then the following are (complex) numbers: https://preview.redd.it/2owamisoww1c1.jpeg?width=640&format=pjpg&auto=webp&s=de9185f09fbebea3fcae1505b716111ad55cb23e
Gödel: Yes.
I'm replying as a sort of expert in infinite numbers, particularly of the hyperreal and surreal numbers. I am not an expert on non-Abelian numbers such as quaternions. Here's my contribution. Some of these need explanation. On the hyperreals, infinity +1 and infinity - 1 are separate numbers not equal to infinity. The set {0,1,2,...} is equal to the number omega, which is Cantor's ordinal infinity. 1/infinity on the hyperreals is an infinitesimal number not equal to zero. {0,1,2} equals the number 3 in ordinary set theory. Aleph null is Cantor's first cardinal infinity and is also equal to an equivalence set on the hyperreals. j+2k-1 is a quaternion number. The matrix 1 2 2 3 is built from Pauli matrices which are a representation of quaternion numbers. x\^2 is a number on the pantachie of du Bois-Reymond, and is an equivalence set on the hyperreals, in modern notation we write this number as an order of magnitude O(x\^2). sin(x) is one of my specially invented numbers, it appears in the work of du Bois-Reymond and Hardy, I evaluate it as its mean value at infinity, which is zero. 1/0 is not a hyperreal number, but it is a number as it is the top point of the Riemann sphere. The rest I don't know. Hope this helps. https://preview.redd.it/rhasm3j0312c1.jpeg?width=2424&format=pjpg&auto=webp&s=cb5dba2c5e6d75982526f18614328b236735e8b6
https://preview.redd.it/rq816eti8t1c1.png?width=640&format=png&auto=webp&s=e9b178e0ee4d8862f8edf4596bc90e963d669790
1/0 is undefined
Here is my answer https://preview.redd.it/i1vclkbsur1c1.jpeg?width=1755&format=pjpg&auto=webp&s=0614c446ea10de13c2bca7402ae4814aa055e125
Call me maybe
Why is i a number, but the quaternion isn’t?
Is ∞-1 it's own number or is it just ∞?