How would Veeky Forums define 'one'? Without using words such as 'single', 'unit' or any other numbers

How would Veeky Forums define 'one'? Without using words such as 'single', 'unit' or any other numbers.

a thing that isnt accompanied by more things

a thing

I thought about calling it the number of elements in a set in which you can't create a random pair of elements. But then you have to define a pair.

"one" can be called a set of identical entities (with respect to some frame of reference) which contains no entities which are the same.

One is the successor of 0, and the identity element of multiplication

you realize that "a" is synonymous with "one", right? right?

"One" is logically impossible because for there to be "one" we must have a second "one" to observe the first "one". But then we have two.

so is "thing."
what's your point?

'thing' doesn't define one as a number

[eqn]\exists X | \forall x, \forall y \in X, x \equiv y|!\exists y \in X \equiv \forall x \in X [/eqn]

Op here.
My question comes from the 'paradox' I encountered a year ago while reading an OSX dictionary: 'compass' and 'north' are defined referring to one another, which makes understanding these two concepts impossible, if you don't know neither.

something

Why in the fuck is this even a question? Why should one care?

A number of points in which two coplanar unperpendicular lines cross

not multiple

because it's Veeky Forums

define two

you could argue that "north" is an axiom, a concept that people just agree to be what it is, but you could say that "north" is the cold area where a magnet points to that is closest to most people on the planet in 1882.

you can't logically reduce define every concept without running into either loops or dead ends. there are just certain things that we accept to be true, especially concepts that can not really be proven, only defined on an abstract level.

that's an axiom. something accepted as true. these are the bedrock of all logic. without them, logic doesn't work. and if they turn out to be false, all logic based on them needs to be revised.

Its the amount you have when you cant have any less without having nothing

4 but with 3 less

The indivisible amount

The first and last thing of something

what...?

your picture.

I thought 0.00000000000000000000000000000...1 was the successor of 0.

Decimals dont really exist. The number that comes after 0 is one, anything else is just taking an arbitrary multiple of 10 and calling it 1

How would you prefer to represent rationals for easy comparison of magnitude? Or is a field that is closed under division not something you are into?

>define one without using the things you use to define it
Fuck off

The way it is is fine, so long as you keep in mind what it is you are "actually" doing so to speak

The multiplicative identity element in [math]\mathbb{C}[/math].

I would define it as {{}}

You know, like we already do you fucking high school dropout.

'one' is /that/ thing that all sets containing exactly one member have in common.

That's the cardinal one, what about the ordinal one?

>I thought
that's where you went wrong

minimum element of the naturals, ainnit Cantor?

>Decimals dont really exist.
Is this a new branch of Terryology?

>Define one without using any of the words that define one
Does everyone here have autism?

Which naturals are you talking about bruh, naturals without zero is plebeian bullshit rooted in historical rejection of zero as a valid and useful concept.

It's also silly to define a number in terms of a set already including it.

All is connected; we are One.

Ra-Teir-Eir

1={{}}

It's actually the cardinality of the set containing the empty set.

Shh, they just learned that construction and are proud of themselves that now they know Mathematical Truth, the only valid construction that could possibly exist.

I've never seen someone so worked up over whether or no the naturals include 0.

I don't see anything wrong with using which ever fits your current situation.

The first sentence was sarcastic. The second is more relevant.

No, I don't think that's right. I've seen them constructed the way I stated.

Also, I think you mean it's the cardinality of the set containing only the empty set.

Yeah, I ignored the second because I don't think you're having a worthwhile discussion

ALONE.

>yeah i ignored the valid point because i didn't like the rest

>>yeah i ignored the valid point because i didn't like the shitpost
and?

lol

If you can't handle one sentence of bullshit prefacing a serious response, you're in the wrong place buddy.

You can define the Natural numbers through set theory.
One is usually the set which contains the empty set.

Mathematicians have thought about these questions more then you would imagine and there are different ways to define the Natural numbers.

Being

>when trolls lose but won't give up
Stop embarrassing yourself

welcome, newfag

What is a set?

3-2

Axiom of empty set:
[math]\exists \phi: \forall x, x \notin \phi [/math]
Axiom of Infinity:
[math]\exists I: \forall x \in I, I \cup \{x\} \subset I[/math]
Define natural numbers
[math]\phi \in \mathbb{N}, \forall x \in \mathbb{N}, \mathbb{N}\cup \{x\} \subset \mathbb{N}[/math]
Define successor function
[math] \mathcal{S}: \mathbb{N} \rightarrow \mathbb{N}, \mathcal{S}(x) = \{x\} \forall x \in \mathbb{N}[/math]
Axiom of unity:
[math] 1 \in \mathbb{N}[/math]
Axiom of induction:
[math]1 \in S \subset \mathbb{N} \wedge (x \in S \Rightarrow \mathcal{S}(x) \in S \forall x \in \mathbb{N}) \Rightarrow S = \mathbb{N}[/math]
1 is the least natural number:
Equivalence of induction with well ordering [math] \Rightarrow \mathbb{N}[/math] is well ordered [math]\Rightarrow \exists 1 \in \mathbb{N}: x \geq 1 \forall x \in \mathbb{N}[/math]

{{}}

One of the most basic mathematics Ideas is the set.

Imagine you have "things" and you put them together and instead of naming calling them "thing a", "thing b", ... you give them all together a name and that is what you call a set.
Then by defining further what exactly set means and what you can do with them you will get to the basis of set theory.

By that way you will soon find what a set of sets is and what empty set means.

nice labia, mate. now answer OP

A set containing an empty set

I don't think that's what he meant.

‘One’ defines an abstract element which cannot be described outside of human baggage terms.

Let’s expand on this…

Take a look at the structure known as addition mudulo two:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0

This structure can be defined using any baggage terms you like, for example:

e x e = e
e x a = a
a x e = a
a x a = e

Or perhaps…

Even and even make even.
Even and odd make odd.
Odd and even make odd.
Odd and odd make even.

It is completely irrelevant which baggage terms we use, as both examples describe the exact same underlying structure which has no intrinsic properties other than the relations between abstract elements.

>an

Yeah, people really aren't getting the premise of this argument.

>How do you define an abstract element?

Anyway you like!

Multiplicative identity

>what is an article
He could just write [math]\{ \emptyset \}[/math] you morons.

[math]\lambda f. \lambda x . x[/math]

Shit.

Add 1 to that.

Undergrad detected.

Take a fucking (proper) Mathematical Logic class; that notation is godawful and flat-out ungrammatical and meaningless.

As my dick, 1 inch

One is the number of earths there are.

Freshman detected

the irreducible quantity of something (though technically no two things are exactly the same)

t. (((wittgenstein)))

The smallest positive integer value.

The multiplicative identity.

Incorrect. 1 is defined as {{}}. We say the cardinality is 1 to mean that there exists a bijection from this set, 1, to itself which is trivially true. That's why we also say for example, {a}, has cardinality 1. Because there is a bijection from {a} to 1 i.e. a bijection from {a} to {{}}.

What does {{}}.mean? I'm guessing it's not a representation of a vulva.

One is the smallest whole presence of an entity.

0 is o, 1 is {o}, 2 is { o, {o} }. Learn you basic maths you baka.

its like computer science. the engine must understand the function, and input to give an output. If the machine questions the input it must ultimately decide to take or leave it ; but leaving it means no input for the fuction, so the presumption must exist for the engine to, well, exist. Am I right or wrong in thinking this?

machines do not question

There is a set containing a set as one of its members. In this case, we have some set containing {} which can be represented as {{}}.

value that adds nothing a another value when you multiply them

to another value*

after 0 before 2

Aristotle pls go

Half of two

0!=1

1 := S(0) : 0 is the empty set,
S(x) := x U {x}

So there is one set containing one set and you use this to define "one"?

floor (log10 (floor (log10 (x))))

>Which naturals
Naturals as in counting numbers.
>naturals without zero
Try counting zero objects.

Unity

the factor shared by all prime numbers

/thread