What are Veeky Forums's preferred axioms?

What are Veeky Forums's preferred axioms?

the axiom that OP is a faggot

Law of non-contradiction
Law of identity

Not really sure what comes after that

>the axiom that OP is a faggot
Why the homophobia?

>Law of identity
overrated

What's overrated?

>What's overrated?
The law of identity.

Correct me if I'm wrong, but since the def'n is
> the law of identity states that each thing is identical with itself.
Whenever you refer to anything, and intend that your audience understand your words/sentences as referring to THAT thing and not to any other thing, you are implicitly relying upon the law of identity, no? Hence by dismissing the law of identity as overrated, you are implicitly relying upon it, as you meant to say that it is the law of identity that is overrated, and not the purple striped pyjamas that are overrated, because the law of identity = the law of identity, and the law of identity != purple striped pyjamas

Feel free to change my mind though

not that guy, but really this is less about the law of identity specifically and more about the contradictions that arise when trying to define a system within the formal context of that system itself.

/thread

Right, but that isn't an argument against the law of identity. The law of identity is still true, afaik, as is the law of non-contradiction. You can't get 'outside' these axioms without contradicting yourself.

>not that guy, but really this is less about the law of identity specifically and more about the contradictions that arise when trying to define a system within the formal context of that system itself.
I'm not a "guy".

Axiom of Choice
Because it is God Like

Sorry, not that M-t-F.

All those that piss off Wildberger crybabies.

>axioms
>not inference rules

modus ponens is GOAT

Extensionality
[math]\forall X\,\forall Y\,[\,X=Y\quad\Leftrightarrow\quad \forall z(z\in X\ \Leftrightarrow\ z\in Y)\,] [/math]
Pairing
[math] \forall x\,\forall y\,\exists Z\,\forall z\,[\,z\in Z\quad\Leftrightarrow\quad z=x ~or~ z=y\,] [/math]
Union
[math]\forall X\,\exists Y\,\forall y\,[\,y\in Y\quad\Leftrightarrow\quad\exists Z(Z\in X {~ and ~} y\in Z)\,][/math]
Empty set
[math]\exists X\,\forall y\,[\,y\notin X\,][/math] this set [math]X[/math] is denoted [math]\emptyset[/math]
Infinity
[math]\exists X\,[\,\emptyset\in X { ~and~ } \forall x(x\in X\Rightarrow x\cup\{ x\}\in X)\,][/math]
Power set
[math]\forall X\,\exists Y\,\forall Z\,[\,Z\in Y\quad\Leftrightarrow\quad \forall z(z\in Z\ \Rightarrow\ z\in X)\,][/math]
Replacement
[math] \forall x\in X\,\exists!y\,P(x,y)\quad \Rightarrow \quad [\,\exists Y\,\forall y\,(y\in Y\ \Leftrightarrow\ \exists x\in X\,(P(x,y)))\,] [/math]
Regularity
[math]\forall X\,[\,X ≠ \emptyset\quad\Rightarrow \quad\exists Y\in X\,(X\cap Y=\emptyset)\,][/math]
Constructibility
[math]V=L[/math]

Define V and L

>Not just using conjunctions and disjunctions

V = the von Neumann universe
L = the constructible universe

Fun fact: You still need an inference rule.

ZFC is for patricians. Only edgy teenagers reject choice.

I prefer my sets measurable.