/mg/ -- Anti-LEM edition

by definition of negation

>by definition of negation
Which definition?

[math]\textit{the}[/math] definition. if something is false, the negation on this something is true and vice versa.

>the definition.
en.wikipedia.org/wiki/Negation#Definition

>No agreement exists as to the possibility of defining negation, as to its logical status, function, and meaning, as to its field of applicability..., and as to the interpretation of the negative judgment

so, contrapositive doesn't work? you say negation isn't defined but countless times again it's application in the classical mathematical sense yields practical results

>so, contrapositive doesn't work?
correct

>you say negation isn't defined
I didn't say that, there are multiple definitions.

>correct
you're wrong. what is this, some Wildbergian type philosophy you're arguing with?

>you're wrong.
What do you mean?

tell me, if a sequence is convergence does this imply it is bounded?

>tell me, if a sequence is convergence does this imply it is bounded?
Yes, but what's the relevance?

would you also agree, that if a sequence is unbounded, then it is divergent?

>would you also agree, that if a sequence is unbounded, then it is divergent?
Yes, but what's the relevance?

Do you know what a counter-example is? I just gave you one. That is textbook example of contrapositive.

>Do you know what a counter-example is?
Do you? You don't need contraposition to prove either of those two statements. Assuming that you can't make use of contraposition is not the same as the contrapositive being false for all true statements.

It's not about the proof of the two statements, rather that both of them are logically equivalent via the contrapositive, which you said doesn't work but I just showed you it does.

>rather that both of them are logically equivalent via the contrapositive, which you said doesn't work but I just showed you it does.
Where did you show it works?

...

You'll have to elaborate on how convergent sequences being bounded and unbounded sequences being divergent implies that given any statement (A -> B), (A -> B) is equivalent to (¬B -> ¬A).

I mean, it's a simple proof by contradiction. If you don't believe in contradiction proof, then all the best but I'll just head on to bed then.

>I mean, it's a simple proof by contradiction.
Feel free to proceed.

en.wikipedia.org/wiki/Contraposition#Simple_proof_by_contradiction

>We also know that B is either true or not true

'night user. Good luck in your studies.

thanks for proving the uselessness of pure math faggotry.

>mfw this thread is too people arguing about the most retarded shit because the first guy did not properly explain that what he meant is that LEM doesn't NEED to work, but we assume it works in our logical system. And the other guy, not knowing this, is posting proofs using our normal logic system and then the first guy dismisses these proofs by simply pointing out that the proofs are on top of normal logic which he is not talking about, but he never properly explained he isn't talking about it.

...

>too

>because the first guy did not properly explain that what he meant is that LEM doesn't NEED to work
I'm not a "guy".

How could I have been more clear?

>mfw this first guy is so embarrassed after noticing he never actually explained himself that the only cover he has is pointing out a typo

I don't want to be mean so just you have something to say I will gift you another typo:

Hey guys, isn't Eminem a good raper?

>Hey guys, isn't Eminem a good raper?
not anymore

>How could I have been more clear?
You were clear to me, but it is clear that the guy you are arguing with did not properly get that. But instead of properly explaining yourself you just followed his rhythm like a little bitch.

>I'm not a "guy".
Mathematically speaking, what do you mean?

>Mathematically speaking, what do you mean?
Guy(me)=0

>Mathematically speaking, what do you mean?
or perhaps keeping in line with the theme of the thread, ¬Guy(me)=1

I don't understand. If Guy an indicator function that gives a 1 whenever the input is a guy or 0 when the input isn't, or is Guy an implicit function that defines the set [math] \{ x \in \mathbb{PEOPLE} : Guy(x) = 0 \} [/math] in the same way you typically implicitly describe a circle? In this sense, wouldn't only guys be roots of the function Guy?

>If Guy an indicator function that gives a 1 whenever the input is a guy or 0 when the input isn't
Quite.

Okay, I see. But then you are defining yourself by what you are not. Could you define yourself by what you are?

Perhaps, a better way of phrasing my question is this: Biologically speaking, what are you?

>Could you define yourself by what you are?
No I can not.

>Biologically speaking, what are you?
Sentient and sapient

>Sentient and sapient
No no no, I need something more specific. Let me ask you again.

When you were born, did you come equipped with the pink fleshy hole that is typically used to put penises inside, that is not the butthole?

>When you were born
I'm not sure what you mean by this?

>entertaining this mentally ill attention whore
/mg/ has fallen

Threadly reminder to work with physicists.

I was trying to remove the ambiguity of you having a pink fleshy hole that is typically used to put penises inside that is not the butthole (I will call it [math] \mathbb{PFHTITUTPPITINTB} [/math] from now on) that you obtained from surgery.

So I mean is that were you born without a Y chromosome?
Are you an XX chromosome?
Biologically, do you not have a penis and were not born with one?
Are you a non-male human that is not a trap or maybe trans? Are you a non-(male or trap or trans) human?
Do you have the same gender as your mom?

Those are all the same question so I expect only one answer.

tranny btfo, probably off to chug pills and cry.

ayo i made an /mg/ discord.

join it for bants and math.

discord.gg/qnyBW3Q

...

It's been a while, but how's everybody's research going?

Currently under review

>Binary valued logics
>not many valued logics
>mfw this thread isn't fuzzy
>mfw this thread isn't modal
>no quantified predicates
>no quantifiers at all

Stop shitting up muh logic.

(∀x)□((◇x=u) ⊃ Fx)

where Fx is a unary relation that asserts that x is a faggot.

Cool, what's it about?

Why would you use homophobic unary relations ?

>not using an inconsistent logic

Intuitionistically you think of OR as a union of open sets in a topological space, AND as intersection. But then you interpret negation as the interior of the complement so in general it's not the whole space.

No.

All of many valued logics, fuzzy logics, modal logics and so on, can be constructed as models within binary value logic. In fact, that is how they are approached.

>thanks for proving the uselessness of pure math faggotry.
Are you okay?

real analysis and algebra quals this week

wish me luck boys

I don't tell you how to be a loser, don't tell me what relations to use.

That's stupid please don't post in my general again.

Congrats on missing the point.

》doing logic instead of math
what's the point?

>That's stupid
Why is that?

Good luck, and remember, always leave a room for epsilon and representation theory makes algebra a hell of a lot easier.

Was the 20th century the greatest century for mathematics? Will it ever be surpassed?

>Will it ever be surpassed?
Yes. I'm surpassing it as we speak.

Assuming a feminist school of relative logic is formed, yes. It will be surpassed by this group equipped with the superior female logic. The pioneers have already started. Just remember Piper Harris or whatever its name is.

So this year I finished my Calc sequence (1,2,3 and Diff Eq) and my Linear Algebra sequence (1,2) and now I found a neat way to combine the theory seen in Linear Algebra with the concepts of Calculus called Differential forms. I'm reading a book on it and I already know what k-forms are and what differential k-forms are and the wedge product and how the derivative on these differential forms look like the divergence, curl and gradient, etc.

My question is, what will I gain from this? I already know all of Calc 3 which means I can solve problems that involve it. But obviously, I learned Calc 3 in the naive "Let's generalize the concepts from Calc 1" way, not with differential forms. Will knowing differential forms enhance my problem-solving skills? Will this new perspective enlighten me to solve harder problems?

how? i really don't get representation theory. Like whats the point even? Nah but srsly please elaborate, maybe i'll even learn something.

Give you a way to study groups using linear algebra. Linear algebra is always easier.

But since finite disjoint sum is the same as finite product of topological spaces then AND and OR would be the same, which they aren't

I'm asked to proof or give a counter example if false.
For a non empty set X
[math]TO\preceq \land S\subseteq X \land S\neq\varnothing\;\implies\;\exists!x:S.\forall y:S.x\preceq y [/math]
or in words( if there is a totally ordered relation on X and S is a non empty subset of X, then there exists a unique x lower bound in S)

Is [math]S=-\infty..0[/math] with [math]X=\mathbb{R}[/math] a valid counterexample?

That girl is very cute. I wish we could hold hands.

She's not real bud, no matter how much math you show her she's not real.

>finite disjoint sum is the same as finite product
it isn't though?

How do you formally prove a negation in intuitionistic logic anyway?

Yes it is, they're isomorphic

To prove not P, assume P and derive a contradiction

It can, people use differential forms to define De Rham Cohomology, doing that allows you to understand properties of the solutions of some important differential equations, the most readily available example is maxwell's equations. This video goes more in depth
youtube.com/watch?v=6qMGz5hCx94&index=3&list=PL7aXC0jU4Qk7K778c5nmgQImd6VKKFMYu

Do you rewrite lecture notes?

It's hard to go into more sophisticated theory (de rham cohomology, etc) without the appropriate analysis and algebra background, much less use them for engineering problems

used to but it takes too much time

#1 it's not disjoint sum, it's the actual sum inside of a single space

#2
>finite disjoint sum is the same as finite product of topological spaces

no it's not. You're thinking of vector spaces.

yes

>actual sum

sorry, meant to say union here

When did you stop doing it?

I was actually thinking about groups. Since direct product is a product and direct sum is a coproduct and direct sum of finitely many groups is the same as product of finitely many groups and I thought that if the product of topological spaces is a product and disjoint sum is a coproduct then it would be similar as with groups and finite product would be isomorphic to finite disjoint sum

Ok what the fug do I need Veeky Forums. I was asking for a PhD position in algebraic geometry and he responds back with this - what is a strong background at a top uni?

I would assume Chapter 2&3 Hartshorne (or equivalent) minimum.

and neither is feminist logic or any of this stupid shit you spergs are arguing about, are you cute irl? r u a chestlet or a titcow?

assuming I complement it with Eisenbud's comm algebra, what other background do i need to start Hartshorne and how long will I take?

Classical Algebraic Geometry would be good for motivation, but desu aside from a few select exercises you don't actually need it.

The same way you do in classical logic.

>She's not real bud
She is though.