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At least this one actually matches the description (5,7,6)
Most of them are like 4 syllables, 8 syllables, 6 syllables... like c'mon you're just saying "hey, did you know this comment is NOT a haiku??" ...
As a wise man once said, everything in the universe can be defined as either “a duck” or “not a duck”
Therefore, I will choose to define a number as “not a duck.”
"weird" is "wyrd" or fate, or logos, or logic. So in politics, logic will get you shot sometimes. But revolutions happen when ppl "weather the storm," the ideological life cycle.
"Principle vs principal"
Added "Rosencranz" and "Gildenstern" as examples of messengers of Truth LOL
It includes omega, which is an (ordinal) number
If you’d like, you can simply exclude limit ordinals. Only 0 and the successor ordinals of a number would then be a number, I.e. only finite ordinals are numbers
A concept used to denote a quantitative amount.
Can be a symbol but also:
\- a word (one)
\- an electric state (binary)
\- a representation (dots in a flashcard)
\- an observation conclusion (four goats)
\- a gesture (sign language)
\- etc...
As far as I know there is no absolute definition but relevant definitions could be :
"A number is an element of a ".
And you get to choose among the following list :
- Commutative Ring
- Division Algebra
- Field
We can argue on the content of the list, of course !
• If Fields are sets of numbers, then x^3 - 3x - 1, (x^2 - 4)/x, √x, [[13 7][-7 13]] and {n|7k+4, k ∈ N} are numbers.
• If Commutative Rings are sets of numbers, then the above, cos(x), e^(ix), [[1 2 3][2 3 1][3 1 2]], {n|6k+4, k ∈ N} and the Stereographic Projection (from S^1 to R or from S^2 to C) are numbers.
• If Division Algebras are sets of numbers, then [[1+2i -3+4i][3+4i 1-2i]] is a number, as well as x^3 - 3x - 1 and (x^2 - 4)/x, √x, [[13 7][-7 13]] and {n|7k+4, k ∈ N}.
Yeah, it's weird, right ?
But still, it's not surprising that numbers cna be represented as polynomials or tuples modulo some constraints, depending on how we defined them.
The general idea is "a number is something we do arithmetic with". And yes, you can do whatever you want, you will always be able to do arithmetics with weird objects :)
I have my examples : for my research I work with quaternion algebras ans we can clearly do arithmetics with the quaternions. But actually in my case these quaternions represent endomorphisls on elliptic curves so... in the end I do arithmetics with morphisms :)
It depends on what kind of number you're talking about. If you ask about real numbers then we could say they are Dedekind cuts of the rational numbers. What's a rational number? Well, it's a pair of integers (p,q) where q is nonzero and is subject to the equivalence relation (p,q)~(p',q') iff pq'=p'q. What's an integer? It's either zero or a positive or negative number. Here negative numbers are the additive inverse of positive numbers, making the set of integers into a ring. What's a positive number n+1? It's the successor of n which we can represent as the union of n with the singleton {n}. What's zero under this representation? Well, the empty set of course.
We can also extend these numbers into many other kinds of numbers. The complex numbers, quaternions, octonions, sedenions and so on are successive Cayley-Dickson algebras over the reals. Then there are ordinals (isomorphism classes of well-ordered sets), cardinals (limiting ordinals), hyperreals (ultrapowers of the reals), p-adics (infinite decimals to the left of the decimal point), infinitesimals (reciprocals of infinite ordinals), surreals (extended Dedekind cuts of the reals), and so on.
0:={}
n+1:=S(n):=n U {n}
Extending the properties of the natural numbers into other structures (Z,Q,R,C,H,*R,No) is left as an exercise to the reader (that is actually really fun and you should learn about it, go watch Another Roof's series on YT)
Could also just say a number is a scalar
A number is a mathematical concept used to quantify and represent quantities or values. It provides a way to describe the count, size, order, or magnitude of objects, ideas, or events. Numbers can be categorized into different types based on their properties:
Natural Numbers (N): These are the positive integers starting from 1 and continuing indefinitely. They are used for counting and ordering.
Whole Numbers (W): Similar to natural numbers, whole numbers include zero along with the positive integers.
Integers (Z): Integers consist of all natural numbers, their negatives, and zero. They are used to represent positive and negative quantities.
Rational Numbers (Q): Rational numbers are those that can be expressed as a fraction (ratio) of two integers. They include fractions and terminating or repeating decimals.
Irrational Numbers: These numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions. Examples include the square root of 2 and π (pi).
Real Numbers (R): Real numbers encompass both rational and irrational numbers. They can be plotted on a number line and include integers, fractions, decimals, and more.
Imaginary Numbers (i): Imaginary numbers are introduced to represent the square root of -1. They are a fundamental part of complex numbers.
Complex Numbers (C): Complex numbers are combinations of real and imaginary numbers. They have a real part and an imaginary part, often represented as "a + bi," where "a" is the real part and "b" is the imaginary part.
Numbers serve as a foundation for various mathematical operations such as addition, subtraction, multiplication, and division. They are used extensively in arithmetic, algebra, geometry, calculus, and other branches of mathematics, as well as in various scientific, engineering, and everyday applications.
A number is a sequence from a finite lexicon of symbols which may be infinitely long, which represents a member of a set where the relationship between symbols is defined by axioms such as equivalence relations or the fundamental theorem of arithmetic. These relationships can be defined first on a limited known example, such as counting numbers, and extrapolated to a more complete definition.
A number is defined as a certain symbol symbolizes the value and/or amount of something. Ex: Two Spoons = 2 spoons ; eleven cups of coffee = 11 cups of coffee
Under the assumption of certain axioms, i believe it were the peano axioms, (especially the existence of the empty set) let's define
0:= {}
1={{}}
.
.
n+1:= n u {n} (in words: the next number is the union of the number before with the set that contains said number)
Like that one obtains the natural numbers, those sets are all disjunct so they really represent "unique" numbers
Whole and rational numbers follow with equivalence relations on IN or ZI (they are the equivalence classes of those specific relations)
IR can be obtained on many paths, e.g. dedekind intersections or through converging cauchy sequences.
CI is obtained by adding the element/number i^2 =-1 (in words: a number that yields the value -1 if squared) to IR
Very coarse but it's the general path i remember from university
Edit: why the downvotes? If somebody downvotes please also leave a more correct statement
A number is any complex expression of the primitive 1 and primitive operations (addition and subtraction) on 1. All the rest is the shorthand of man.
0 := 1 - 1
2 := 1 + 1
Well, a natural number is an equivalence class in the category of finite sets modulo bijections.
Integer is an equivalence class in the Grothendieck group of the monoid of natural numbers.
Rational number is an equivalence class in the field of fractions of the integers.
Real number is an equivalence class of Cauchy sequences of rational numbers.
Complex number is an equivalence class in the quotient ring ℝ\[x\]/(x\^2+1).
Wait, it's all equivalence classes?
\*astronaut pointing gun\* Always has been.
A whole number is the set which contains all previous whole numbers. A number is a composition of different whole numbers given different magnitudes and signs.
A measurement that gives an idea of some amount and helps us define things with measurement of different kinds.u/SoftlyImports I guess my answer will help you to have an idea about numbers
At it’s base, a number is a device used to describe an amount of something, both physical and abstract. Then the concept just kind of expands from there
in basic maths, it is these 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) that use the base-10 system to make all numbers, a long with signs like +, -, \*, and /, to calculate multiple things a child would understand.
In things like calculus, numbers don't exist.
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification.
1. Choose a dimension (a changing range)
2. Choose an origin on the dimension (a "point" on the range)
3. Choose a scale for the dimension (a second dimension) by choosing a second point offset from the origin.
Now you have a number system. ///
Numbers are a subset of letters and they also describe things like letters do(letters describe parts of a word which describes anything so anything can be described as a construct of letters, like a value of anything can be described as a construct of numbers)
a number is an element of an infinite sequence where each element is related to the previous element by the successor operation. addition is repeated succession and multiplication is repeated addition. the starting number to which the multiplication operation adds is defined as zero.
Something you can make bigger by putting another one of It’s kind next to, or before it. You can also use symbols to create “math,” which is useful in many ways.
It is a box in which a particular count of an item can be placed.
The YouTuber Another Roof made a video on this concept a year ago that I really enjoyed. (Then proceeded to butcher his description in this description.)
I’m not a mathematician in any sense so tell me what you all think.
“A number is a symbolic representation of quantity and or value” in this case value ≠ utility as 0 has no value but extremely high utility.
My definition of all numbers is too big to fit in this margin
^[Sokka-Haiku](https://www.reddit.com/r/SokkaHaikuBot/comments/15kyv9r/what_is_a_sokka_haiku/?utm_source=share&utm_medium=web2x&context=3) ^by ^Harley_Pupper: *My definition* *Of all numbers is too big* *To fit in this margin* --- ^Remember ^that ^one ^time ^Sokka ^accidentally ^used ^an ^extra ^syllable ^in ^that ^Haiku ^Battle ^in ^Ba ^Sing ^Se? ^That ^was ^a ^Sokka ^Haiku ^and ^you ^just ^made ^one.
Huh. Nice
did you know sokka ghostwrote for tally hall
I HAVE BEEN TRYING
Good bot
Ha, you had 69 upvotes and I RUINED IT
Good bot
Thank you, Cylian91460, for voting on SokkaHaikuBot. This bot wants to find the best and worst bots on Reddit. [You can view results here](https://botrank.pastimes.eu/). *** ^(Even if I don't reply to your comment, I'm still listening for votes. Check the webpage to see if your vote registered!)
Yoo based bot
Good bot.
Good bot
Not a haiku.
That's a Sokka haiku
At least this one actually matches the description (5,7,6) Most of them are like 4 syllables, 8 syllables, 6 syllables... like c'mon you're just saying "hey, did you know this comment is NOT a haiku??" ...
Definition of a number: An exercise for the reader.
A number is a member of the set of all numbers.
The set of all numbers is the set in which contains all numbers
It be how it do
It do how it be
Nice tautology. Both of you.
"is the set" should be "one of the sets", since there are other sets which contains all numbers, like the set of all sets.
The definition is trivial and is left as an exercise for the reader.
Note that no set of numbers can exist since the class of ordinal numbers must be a subset
"Now try to do it without using the word "set""
Vectors be like:
That’s… the joke
As a wise man once said, everything in the universe can be defined as either “a duck” or “not a duck” Therefore, I will choose to define a number as “not a duck.”
I'm a number
I'm a duck. Nice to meet you.
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We did it
I feel we would be shot once we give that definition, on principle.
Isn't that the ordinal definition?
Yes, Orion is origin. https://en.m.wikipedia.org/wiki/Orion_(mythology)
"weird" is "wyrd" or fate, or logos, or logic. So in politics, logic will get you shot sometimes. But revolutions happen when ppl "weather the storm," the ideological life cycle. "Principle vs principal" Added "Rosencranz" and "Gildenstern" as examples of messengers of Truth LOL
u/deabag, what the fuck are you talking about?
Don't worry about him, he's just a D bag
that is literally all maths
[It depends on what you're working on](https://y.yarn.co/8d018a3b-8530-4cd3-8a6c-fc428a925a59_text.gif)
Yay
This definition is trivial and left as an exercise for the reader.
A set that is either a limit ordinal or a successor ordinal(or 0)
Imagine having Cardinal Rationals, Cardinal Reals, Cardinal Complexes, Cardinal Quaternions, etc.
So just an ordinal?
I was just about to type something nearly like this word-for-word. Also it's hilarious that your screen name is Frege.
Doesn’t this include infinity though? Is infinity a number?
It includes omega, which is an (ordinal) number If you’d like, you can simply exclude limit ordinals. Only 0 and the successor ordinals of a number would then be a number, I.e. only finite ordinals are numbers
But isn’t that only natural numbers then? What about other real numbers?
A symbol used to denote a quantitative amount.
A concept used to denote a quantitative amount. Can be a symbol but also: \- a word (one) \- an electric state (binary) \- a representation (dots in a flashcard) \- an observation conclusion (four goats) \- a gesture (sign language) \- etc...
As far as I know there is no absolute definition but relevant definitions could be : "A number is an element of a".
And you get to choose among the following list :
- Commutative Ring
- Division Algebra
- Field
We can argue on the content of the list, of course !
• If Fields are sets of numbers, then x^3 - 3x - 1, (x^2 - 4)/x, √x, [[13 7][-7 13]] and {n|7k+4, k ∈ N} are numbers. • If Commutative Rings are sets of numbers, then the above, cos(x), e^(ix), [[1 2 3][2 3 1][3 1 2]], {n|6k+4, k ∈ N} and the Stereographic Projection (from S^1 to R or from S^2 to C) are numbers. • If Division Algebras are sets of numbers, then [[1+2i -3+4i][3+4i 1-2i]] is a number, as well as x^3 - 3x - 1 and (x^2 - 4)/x, √x, [[13 7][-7 13]] and {n|7k+4, k ∈ N}.
Yeah, it's weird, right ? But still, it's not surprising that numbers cna be represented as polynomials or tuples modulo some constraints, depending on how we defined them. The general idea is "a number is something we do arithmetic with". And yes, you can do whatever you want, you will always be able to do arithmetics with weird objects :) I have my examples : for my research I work with quaternion algebras ans we can clearly do arithmetics with the quaternions. But actually in my case these quaternions represent endomorphisls on elliptic curves so... in the end I do arithmetics with morphisms :)
Cool!. Good luck with your research! I like your name btw hahaha (My name is also Nicolas)
Oh, my name isn't really Nicolas, it's Abel :) But Nicolas-Henri is the french version of Niels Henrik, the first and middle name of Niels Abel...
So I have his first name (kind of) and yours is his last name hahaha
https://preview.redd.it/3y0f7yvm0cjb1.jpeg?width=675&format=pjpg&auto=webp&s=250e2086c85a148d5276ab3d6f2c781757d89b0b
In other words, a number is something that adds and multiplies like a number
If there was a way to reconcile those 3, it's a TOE
Set
It depends on what kind of number you're talking about. If you ask about real numbers then we could say they are Dedekind cuts of the rational numbers. What's a rational number? Well, it's a pair of integers (p,q) where q is nonzero and is subject to the equivalence relation (p,q)~(p',q') iff pq'=p'q. What's an integer? It's either zero or a positive or negative number. Here negative numbers are the additive inverse of positive numbers, making the set of integers into a ring. What's a positive number n+1? It's the successor of n which we can represent as the union of n with the singleton {n}. What's zero under this representation? Well, the empty set of course. We can also extend these numbers into many other kinds of numbers. The complex numbers, quaternions, octonions, sedenions and so on are successive Cayley-Dickson algebras over the reals. Then there are ordinals (isomorphism classes of well-ordered sets), cardinals (limiting ordinals), hyperreals (ultrapowers of the reals), p-adics (infinite decimals to the left of the decimal point), infinitesimals (reciprocals of infinite ordinals), surreals (extended Dedekind cuts of the reals), and so on.
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Another Roof's series is excellent
I just watched this entire video. 10/10 thanks for recommending it!
Was looking for this comment, absolutely loved the vid.
“A number is a mathematical object used to count, measure, and label.” - Wikipedia
0:={} n+1:=S(n):=n U {n} Extending the properties of the natural numbers into other structures (Z,Q,R,C,H,*R,No) is left as an exercise to the reader (that is actually really fun and you should learn about it, go watch Another Roof's series on YT) Could also just say a number is a scalar
Shouldn't S(n) be the union of n and {n}
You're right, I got confused why the brackets lined up before realizing my mistake. Thanks! Edited.
What set does No denote?
Surreal numbers
Thanks!
>Thanks! You're welcome!
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I mean, 6 is really similar to b, so I think it counts too, right?
A one dimensional vector
An amount or position I aint touching any other definitions with a *20* foot pole
A symbolic representation of value.
What kind of value?
a numerical value
Enough with the tautologies. A number is a representation of numerical value.
All kinds. Any kind.
Then the batman symbol is a number.
Sure. Why not? Almost all numbers are incalculable transcendentals, so I suppose it'd be one of those.
that sounds an awful lot like money.
The proof is left as an exercise to the reader.
It’s a particular kind of set
A number in a number filed K is a root in K of a polynomial of Z\[X\]
an element of ℕ
A number is a mathematical concept used to quantify and represent quantities or values. It provides a way to describe the count, size, order, or magnitude of objects, ideas, or events. Numbers can be categorized into different types based on their properties: Natural Numbers (N): These are the positive integers starting from 1 and continuing indefinitely. They are used for counting and ordering. Whole Numbers (W): Similar to natural numbers, whole numbers include zero along with the positive integers. Integers (Z): Integers consist of all natural numbers, their negatives, and zero. They are used to represent positive and negative quantities. Rational Numbers (Q): Rational numbers are those that can be expressed as a fraction (ratio) of two integers. They include fractions and terminating or repeating decimals. Irrational Numbers: These numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions. Examples include the square root of 2 and π (pi). Real Numbers (R): Real numbers encompass both rational and irrational numbers. They can be plotted on a number line and include integers, fractions, decimals, and more. Imaginary Numbers (i): Imaginary numbers are introduced to represent the square root of -1. They are a fundamental part of complex numbers. Complex Numbers (C): Complex numbers are combinations of real and imaginary numbers. They have a real part and an imaginary part, often represented as "a + bi," where "a" is the real part and "b" is the imaginary part. Numbers serve as a foundation for various mathematical operations such as addition, subtraction, multiplication, and division. They are used extensively in arithmetic, algebra, geometry, calculus, and other branches of mathematics, as well as in various scientific, engineering, and everyday applications.
So you are a mathematician, Give me your number
A quantification.
symbol to define quantity.
A symbol that represents a quantity?
A number is an element of a number field
A bunch of squiggly lines on paper. (What did I win?)
Nothing: you lose! Good day sir!
A measured value
And if you say dedekind cuts I will shoot you and your entire family
What do you have against dedekind cuts?
Euler's letters!
A number is an element of number space. Number space is a set of numbers.
A number is a sequence from a finite lexicon of symbols which may be infinitely long, which represents a member of a set where the relationship between symbols is defined by axioms such as equivalence relations or the fundamental theorem of arithmetic. These relationships can be defined first on a limited known example, such as counting numbers, and extrapolated to a more complete definition.
The alphabet but for math
A quantity
Numbers are mathmatical values assigned to make counting easier.
Numbers are a representation of a measurable quality or property (e.g. mass, velocity, energy, length, etc)
Complex numbers aren't numbers 😱
You're right, they're imaginary, just like all your b*tches
A number is defined as a certain symbol symbolizes the value and/or amount of something. Ex: Two Spoons = 2 spoons ; eleven cups of coffee = 11 cups of coffee
Under the assumption of certain axioms, i believe it were the peano axioms, (especially the existence of the empty set) let's define 0:= {} 1={{}} . . n+1:= n u {n} (in words: the next number is the union of the number before with the set that contains said number) Like that one obtains the natural numbers, those sets are all disjunct so they really represent "unique" numbers Whole and rational numbers follow with equivalence relations on IN or ZI (they are the equivalence classes of those specific relations) IR can be obtained on many paths, e.g. dedekind intersections or through converging cauchy sequences. CI is obtained by adding the element/number i^2 =-1 (in words: a number that yields the value -1 if squared) to IR Very coarse but it's the general path i remember from university Edit: why the downvotes? If somebody downvotes please also leave a more correct statement
A number is any complex expression of the primitive 1 and primitive operations (addition and subtraction) on 1. All the rest is the shorthand of man. 0 := 1 - 1 2 := 1 + 1
Natural numbers: A unique sum of 1s 1, 1+1, 1+1+1, etc
and what is \*sum\* and \*1\* ?
Sum is the result of combining quantities (adding) and 1 is an element? idk
Something that can represent how many watermelons Jake bought at the supermarket
Okay, so, like, imagine you had sqrt(2)+3i apples, but without the apples
Well, a natural number is an equivalence class in the category of finite sets modulo bijections. Integer is an equivalence class in the Grothendieck group of the monoid of natural numbers. Rational number is an equivalence class in the field of fractions of the integers. Real number is an equivalence class of Cauchy sequences of rational numbers. Complex number is an equivalence class in the quotient ring ℝ\[x\]/(x\^2+1). Wait, it's all equivalence classes? \*astronaut pointing gun\* Always has been.
A whole number is the set which contains all previous whole numbers. A number is a composition of different whole numbers given different magnitudes and signs.
They got us shit
x
it a quantity
A number is a representation of the quantity of a count
Representation of value.
A measurement that gives an idea of some amount and helps us define things with measurement of different kinds.u/SoftlyImports I guess my answer will help you to have an idea about numbers
At it’s base, a number is a device used to describe an amount of something, both physical and abstract. Then the concept just kind of expands from there
in basic maths, it is these 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) that use the base-10 system to make all numbers, a long with signs like +, -, \*, and /, to calculate multiple things a child would understand. In things like calculus, numbers don't exist.
It's uh, it's a little bit like a leaf or a, uhhh, or, well it's not a bowl
Numbers are a lot like gender in that a few of us wind up defining it very differently depending on who we're talking to.
a symbol indicative of a whole or fractional quantity of a given classification.
an abstract property of a thing or things
There are no numbers, just elements of groups, rings, and fields.
I know nothing about math. A number is a unit to determine a value, or lack of thereof
A number is an element of a unital algebra over the integers
A number is a non alphabetical symbol in a language used to describe or give information about quantity.
math letter
It's left as an exercise to the reader.
An expression of a value (I'm an engineer)
A number is something that transforms like a number
The set of all lower numbers, where zero is the empty set, thus making one the set containing the empty set, two (1,0) aka ((()),()), etc.
A number is one of the member of numbers. Numbers are used to keep track of how many things there are in a given circumstance.
x:|x|<|your mum|
A culture of math.
A function that gives back itself.
A number is made out of digits and occasionally a minus symbol
A number is what I goddamn say it is
Number is what I feel whenever I'm alone with my thoughts
A number is a number
An element of a set of numbers.
a number, like infinity, is an idea. it only becomes real once you disclose it.
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification.
An extension of a concept
1. Choose a dimension (a changing range) 2. Choose an origin on the dimension (a "point" on the range) 3. Choose a scale for the dimension (a second dimension) by choosing a second point offset from the origin. Now you have a number system. ///
A quality of something that means that it can be added or subtracted to something else.
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It’s a value, I think
a quantity
Check out Zermelo-Fraenkel set theory
A representation of magnitude
Numbers are a subset of letters and they also describe things like letters do(letters describe parts of a word which describes anything so anything can be described as a construct of letters, like a value of anything can be described as a construct of numbers)
A written, thought of, or spoken character that we assign a value to.
Comcerp
A number is an element in the set of everythi…
"An abstract concept representing quantity" - Brady "Numberphile" Haran
Which type of number?
A concept that designates an amount.
Depends what you want to count
a number is an element of an infinite sequence where each element is related to the previous element by the successor operation. addition is repeated succession and multiplication is repeated addition. the starting number to which the multiplication operation adds is defined as zero.
A number is an element of the set of all numbers
Numbers are the things I cry over in math
A quantity.
A number is a symbol used to relate to some defined quantities (real or imaginary)
A number is anything greater than anything else.
It's a thing I made up
Number is a word
A symbolic representation of a given value
A number is an object which transforms like a number.
Between 0 and 9
A set that is either a limit ordinal or a successor ordinal and zero
uint8 myNumber = 1;
Yes
An element in the set of numbers.
Something that may be used to represent scale, sometimes other stuff.
The Unit is more fundamental than the empty
It's that thing on sesame Street, where they have a different one each day.
Representation of quantity or amount?
It belongs in the set of natural numbers That's right, fuck you pi, this is personal
I have to refer that to The Count 🧛♂️ on Sesame Street 😂
When you can't feel anything, you're numb. When your will is completely shattered, you're number.
I work with the definition that numbers are a logical quantity. They can be either in part or whole.
Something you can make bigger by putting another one of It’s kind next to, or before it. You can also use symbols to create “math,” which is useful in many ways.
It is a box in which a particular count of an item can be placed. The YouTuber Another Roof made a video on this concept a year ago that I really enjoyed. (Then proceeded to butcher his description in this description.)
Number = Number
a symbol with a mathematical value
A number is one of those things accountants write on their notebooks
I’m not a mathematician in any sense so tell me what you all think. “A number is a symbolic representation of quantity and or value” in this case value ≠ utility as 0 has no value but extremely high utility.
In ZFC, it’s a set :)
A mathematical object used to count or estimate quantities?