How would /sci/ define 'one'? Without using words such as 'single', 'unit' or any other numbers.
a thing that isnt accompanied by more things
>>8152587
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.
>>8152587
"one" can be called a set of identical entities (with respect to some frame of reference) which contains no entities which are the same.
>>8152587
One is the successor of 0, and the identity element of multiplication
"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.
>>8152606
so is "thing."
what's your point?
>>8152626
'thing' doesn't define one as a number
>>8152587
[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.
>>8152587
something
>>8152587
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
>>8152636
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.
>>8152587
Its the amount you have when you cant have any less without having nothing
4 but with 3 less
>>8152587
The indivisible amount
The first and last thing of something
>>8152797
what...?
>>8152587
your picture.
>>8152604
I thought 0.00000000000000000000000000000...1 was the successor of 0.
>>8152965
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
>>8152992
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?
>>8152587
>define one without using the things you use to define it
Fuck off
>>8153001
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].
>>8152587
I would define it as {{}}
You know, like we already do you fucking high school dropout.
>>8152587
'one' is /that/ thing that all sets containing exactly one member have in common.
>>8153062
That's the cardinal one, what about the ordinal one?
>>8152965
>I thought
that's where you went wrong
>>8153063
minimum element of the naturals, ainnit Cantor?
>>8152992
>Decimals dont really exist.
Is this a new branch of Terryology?
>>8152587
>Define one without using any of the words that define one
Does everyone here have autism?
>>8153071
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
>>8152587
1={{}}
>>8153196
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.
>>8153088
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.
>>8153228
The first sentence was sarcastic. The second is more relevant.
>>8153196
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.
>>8153231
Yeah, I ignored the second because I don't think you're having a worthwhile discussion
ALONE.
>>8153235
>yeah i ignored the valid point because i didn't like the rest
>>8153318
>>yeah i ignored the valid point because i didn't like the shitpost
and?
>>8153323
If you can't handle one sentence of bullshit prefacing a serious response, you're in the wrong place buddy.
>>8152587
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
>>8153345
>when trolls lose but won't give up
Stop embarrassing yourself
>>8153358
welcome, newfag
>>8153355
What is a set?
>>8152587
3-2
>>8152587
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]
>>8152587
{{}}
>>8153427
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.
>>8153510
nice labia, mate. now answer OP
>>8152587
A set containing an empty set
>>8153080
I don't think that's what he meant.
>>8152587
‘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.
>>8153644
>an
>>8153773
Yeah, people really aren't getting the premise of this argument.
>>8152587
>How do you define an abstract element?
Anyway you like!
>>8152587
Multiplicative identity
[math]\lambda f. \lambda x . x[/math]
>>8154022
Shit.
Add 1 to that.
>>8153629
Undergrad detected.
>>8153473
Take a fucking (proper) Mathematical Logic class; that notation is godawful and flat-out ungrammatical and meaningless.
>>8152587
As my dick, 1 inch
One is the number of earths there are.
>>8154066
Freshman detected
the irreducible quantity of something (though technically no two things are exactly the same)
>>8154066
t. (((wittgenstein)))
>>8152587
The smallest positive integer value.
>>8152587
The multiplicative identity.
>>8153196
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 {{}}.
>>8154352
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.
>>8152671
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?
>>8154501
machines do not question
>>8154370
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
>>8154525
to another value*
after 0 before 2
>>8152608
Aristotle pls go
Half of two
0!=1
1 := S(0) : 0 is the empty set,
S(x) := x U {x}
>>8154522
So there is one set containing one set and you use this to define "one"?
>>8152587
floor (log10 (floor (log10 (x))))
>>8153088
>Which naturals
Naturals as in counting numbers.
>naturals without zero
Try counting zero objects.
Unity
the factor shared by all prime numbers
>>8155385
/thread
>>8152629
Yes it does you fucking autist.
Thing has the implicit definition of border/limit, so you can differentiate what is that thing and what is not.
That also creates the definition of unit.
>>8152587
How would you define "OP" without using the word faggot?
>protip you can't
>lelele
That's you.
>>8154066
I agree with you bb, that notation is bad.
>>8152587
The amount of balls hitler had
