/sci/ - Science & Math

>>9210619
Definition.
[math]S(\{\emptyset\}) = \{\emptyset, \{\emptyset\}\}[/math]

Qed.

Evaluate the left side and you get 2

>>9210626
Oh tru

ZFC proves that PA has a model. PA proves 1+1=2, so it's true.

>>9210619
there's one person in a room and then another person comes in the room... how many people are in the room now?

>>9210626
it even works if you evaluate the right side

It's easy: http://us.metamath.org/mpeuni/pm110.643.html

>>9210619
This

Explain to a brainlet like me what a proof is and why 1+1=2 isn't sufficient to prove that one plus one equals two

This is an example of the addition axiom. There is no mathematical proof.
>The additive axiom in mathematics: if equal numbers are added to equal numbers, the results are equal. a+b=c+d
An axiom is an assumption. To prove it is wrong you would also need an to make an assumption. Which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove. Then you would need to prove the assumption you needed to prove you assumption which you would then need to prove...

>>9211844
lel xD ebin engineer maymay bro *highfive*

>>9210625
you're fucking retarded
being the successor has nothing to do with addition; the two are defined entirely separately and, in general, ordinal addition is a pain in the ass
but you'd know that if you weren't just a pseud who browses wikipedia entries to larp

>>9211934
>the addition axiom
kill yourself

>>9210728
nice.

>>9211934
strongly consider suicide.

no vector spaces please

>>9211977
S(x) := x u {x}
x + 0 := x
x + S(y) := S(x) + y
x + sup U := sup (x + U)
HURRRRRRRRRRRR

>>9211990
>i call out an egregious mistake
>he corrects it
>somehow this makes ME look bad
sasuga, anon

>>9212001
>being the successor has nothing to do with addition
>I WAS JUST PRETENDING TO BE RETARDED

>>9212013
>the two are defined separately
but you aren'y pretending to be illiterate

>>9212018
>being the successor has nothing to do with addition
>the two are defined separately
see >>9211990

>>9211256
Depends on if the people reproduce before you count them

Also are there any negative people in the room?

>this autism

pure math homosexuals

>>9212021
see >>9212026

>>9211887
Define 1, define 2, define what '+' means and define what '=' means. Then using the properties of '+' and '=', you need to show how they can lead to 1 + 1 = 2. You might say it's common sense what they mean, but a lot of things that we think are obviously true turn out to be false.

>>9210619
count to 2.

>>9210619
I have one chair {1c}, you have one chair {1c}

If I ask you to give me {1c}

It will be 0+{1c}={1c}

Then, ∑{c} = {1c} +{1c} = {2c}

==> 1+1=2

>>9212816
For that you need to prove that 1*chair+1*chair=2*(chair)

>>9212866
Fuck off

>>9210619
I could do that very easily but first you'd have to define mathematically what 1 and 2 and + are. See >>9211977

>>9212881
>mad because his shitty physical intuitions don't help him prove things
*laughs maniacally*

>>9212898
clean, simple, and short
nice.

>>9212898

can we have the same in modern notation?

>>9210728
ZFC is inconsistent.

>>9211934
>axiom
Subhuman detected.

Prove that [math]1 \neq 0[/math] without appealing to Peano arithmetic or any other similar axiomatization.

You have one banana. You have another banana. Put them side by side and what do you see? Two bananas.
There's your proof.

>>9213123
Still holds, since inconsistent systems prove anything.

>>9213255
>Still holds
I didn't claim it doesn't hold. Read my post carefully, engineer.
> inconsistent systems prove anything.
Only assuming they are at least as powerful as intuitionistic logic.

>>9213242
>There's your proof.
>that's a """proof"""
you're a special kind of retard, aren't ya

>>9213321
How's that not a proof? You have one banana and then add on another. Now, unless some cunt's gone and stolen you bananas, you have two. SOLID PROOF

>>9213294
>I didn't claim it doesn't hold
Then your post is a non-sequitur.
>Only assuming they are at least as powerful as intuitionistic logic.
Which ZFC is by definition.

>>9213123
let's see your proof, tough guy

>>9213583
That's not a proof, it's an example to help illustrate the concept that 1+1=2. The equation still needs to be proven though.

>>9213591
>Then your post is a non-sequitur.
My post merely says that you shouldn't care about what ZFC proves since it's inconsistent.
>ZFC
>systems
Since when is ZFC a "systems"?

>>9213615
Your proof is that you can add one banana onto another and get two bananas.

>>9213625
this isn't even good bait

2x=2
x=1
QED

>>9212898
Oh, that mastodontic book that was shreded by Gödel in a simple elegant paper.

>>9213136
Easy, if we use a ring... Oh fuck!

>>9213594
The proof is trivial. Assume [math]Con(ZFC)[/math] holds, then the following is a long exact sequence in [math]\mathbf{Lang}[/math]:

[math]\cdots \longrightarrow 0 \longrightarrow \mathbb{Q} \otimes_\mathbb{Z} \bigoplus_{\alpha \in \mathbb{R}}^{\infty + \infty^\infty} \mathbb{Z}/p\mathbb{Z} \longrightarrow Con(ZFC) \overset{\xi^\infty} \longrightarrow Con(ZFC + AD) \longrightarrow \Lambda_\omega(H_p(ZFC)) \longrightarrow 0 \longrightarrow \cdots[/math]

Clearly [math]\Lambda_\omega(H_p(ZFC)) \cong 0[/math], since [math]\Lambda_\omega[/math] is a left-adjoint and [math]H_p(ZFC)[/math] is evidently initial in [math]\mathbf{Ab}[/math].
We also have that [math]\mathbb{Q} \otimes_\mathbb{Z} \bigoplus_{\alpha \in \mathbb{R}}^{\infty + \infty^\infty} \mathbb{Z}/p\mathbb{Z} \cong 0[/math] (trivially).

Thus the sequence below is exact as well.
[math]\cdots \longrightarrow 0 \longrightarrow 0 \longrightarrow Con(ZFC) \overset{\xi^\infty} \longrightarrow Con(ZFC + AD) \longrightarrow 0 \longrightarrow 0 \longrightarrow \cdots[/math]

Exactness trivially implies that the morphism [math]\xi^\infty[/math] is in fact an isomorphism, which trivially means [math]Con(ZFC) \cong Con(ZFC + AD) [/math], but AD is inconsistent with
AC, so [math]Con(ZFC + AD) \cong 0[/math].

Thus by transitivity and symmetry of isomorphism we trivially conclude [math]Con(ZFC) \cong 0[/math]. So we have contradiction in the form of [math]Con(ZFC) \land \neg Con(ZFC)[/math] which concludes the proof of the inconsistency of ZFC.

>>9214185
you're a colossal fucking retard

>>9214185
What field of math is this?

>>9214194
applied memetics by some faggot who's learning some category theory or homolical algebra

>>9214185
This is 100% accurate.

Define: Precision.

>>9214206
made me kek, thanks and nice timing. see? your posts can actually be funny instead of plain dumb

>>9214191
That's a rude thing to say, anon. Do you not know anything?
>>9214194
The proof uses basic logic and category theory as well as trivial results about abelian groups.

>>9214218
I never believed them to be either/or.

Careful though, don't mention me 'too' directly or else someone will think we're trying to explain some sort of cosmic joke.

[math]z^*=z \exp \left(-2 i \left(\arg (z)-\pi \left\lfloor \frac{\arg (z)+\pi }{2 \pi }\right\rfloor \right)\right)[/math]

>>9214238
[math]\iota \unicode{f4a2}\vartheta[/math]

We literally cannot count beyond 1.

Binary is where it's at.

>>9214246
[math]\iota \unicode{f4a2}\vartheta \left| \pi \text{$\_$r}\right| \int \Delta f \, df[/math]

>>9214270

>>9214285
There. That's that thread completed.

>>9214194
it's schizophrenic personality disorder
quite common amongst drooling retards like that poster

>>9210619
For you OP: [math]\vartheta \left| \pi \text{$\_$r}\right| \int \Delta f \, df=\frac{1}{2} \pi \Delta f^2 \vartheta \left| \text{$\_$r}\right| +\text{constant}[/math]

Question : Answer

>>9214305
Sorry, forgot to add.

Math = Question : Answer + I (Self)

Physics = Question : Answer + Observers (Pervert)

Science = Question : Answer + C (Sight)

>>9214313
1 + 1 = 2

I = 1
Them = You - I
Us = I + You
We = Us + You

You + Me = Thus

Now it's your turn.

>>9210619
Lrn2principia fgt pls