/sci/ - Science & Math

[Anonymous No.9870660]

>assume

[Anonymous No.9870678]

>>9870660
>let

[Anonymous No.9870683]

>fix

[Anonymous No.9870686]

>suppose

[Anonymous No.9870689]

>>9870660
>suppose

[Anonymous No.9870692]

>imagine

[Anonymous No.9870698]

>Take

[Anonymous No.9870699]

>For

[Anonymous No.9870707]

>to the contrary

[Anonymous No.9870713]

>we

[Anonymous No.9870718]

>it is trivial that

[Anonymous No.9870767]

>consider

[Anonymous No.9870809]

>>9870660
>If this is the case, then we are done. Otherwise,

[Anonymous No.9870811]

>>9870809
>Hence

[Anonymous No.9870837]

>>9870811
pierce is a god

[Anonymous No.9870844]

>wlog

[Anonymous No.9870847]

>>9870837
Agreed.

>by way of contradiction,

[Anonymous No.9870898]

>For each

[Anonymous No.9870917]

>prove it yourself as an exercise

[Anonymous No.9871198]

>whence
>wherefore
>hitherto

[Anonymous No.9871211]

Okay, so who is it? God help I will chop your tiny dick off if you’re a cat fish.

[Anonymous No.9871516]

>assume contrariwise

[Anonymous No.9871608]

>QED

[Anonymous No.9871642]

>>9870660

>Presidential election results

[Anonymous No.9871666]

Can someone explain this meme to me?

[Anonymous No.9871699]

>define

[Anonymous No.9871701]

>>9870660
>explain

[Anonymous No.9871703]

>thusly

[Anonymous No.9871709]

>prove

[Anonymous No.9871711]

>>9871666
>explain

[Anonymous No.9871716]

>>9870660
>choose an infinite number of arbitrary objects

[Anonymous No.9871720]

>define

[Anonymous No.9871723]

>associate to each

[Anonymous No.9871748]

>>9871642
You don't get it at all. Fuck off with that shit.

>>9871666
Lurk more and read a math textbook while you're at it.

[Anonymous No.9871750]

>>9870660
>such that

[Anonymous No.9871769]

>>9871666
>Can

[Anonymous No.9871774]

>>9871748
someone's buttmad

[Anonymous No.9871777]

>>9871716
rare, but good

[Anonymous No.9871795]

>>9871666
what are you? dirty humanities or law fag?

[Anonymous No.9871839]

>that satisfies

[Anonymous No.9871842]

>BRAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP

[Anonymous No.9871863]

> Suppose we have a rope of infinite length in a vacuum

[Anonymous No.9871964]

>>9871863
that's not the meme, brainlet

[Anonymous No.9871974]

>>9870660
>if and only if

[Anonymous No.9871976]

>[math] \square [/math]

[Anonymous No.9871980]

>>9870660
clearly, can be easily shown

[Anonymous No.9871983]

> trivial

[Anonymous No.9871984]

it's trivial

the proof is left as an exercise to the reader

[Anonymous No.9871989]

"Clearly ..."
"Obviously ..."
"It is self-evident that ..."
"It's trivial that ..."

t. Hand-Waving

[Anonymous No.9871996]

>the proof is badly printed and illegible

[Anonymous No.9872010]

>using the commonly known result

[Anonymous No.9872167]

>>9870660
>In this case.
>Case.

DO I LOOK LIKE A LAWYER TO YOU!?
What the fuck did you just fucking say about me, you little starting condition? I’ll have you know I graduated top of my class in the MIT, and I’ve been initiated in numerous secret techniques on Al-Gebra, and I have over 300 confirmed integrations. I am trained in gorilla mathematics and I’m the top math wiz in the entire set of US computational forces. You are nothing to me but just another equation. I will solve you the fuck out with precision the likes of which has never been seen before on this Earth, mark my fucking definitions. You think you can get away with simplifying that fraction that way over the Internet? Think again, factorial. As we speak I am contacting my secret network of underground mathematicians across the world and your domain is being traced right now so you better prepare for the tangent, maggot. The tangent that wipes out that little unknown variable you call your life.You’re fucking summed, sequence. I can be anywhere, anytime, and I can solve you in over seven hundred ways, and that’s just with my pen and paper. Not only am I extensively trained in calculating by hand, but I have access to the entire arsenal of the Texas Instruments Calculator Corps and I will use it to its full extent to wipe your miserable x's off the face of the page, you little inkstain. If only you could have known what unholy differentiation your little “trigonometric” problem was about to bring down upon you, maybe you would have held your exponential range. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn polynomial. I will prove fury all over you and you will drown in it. You’re solved dead, limit.

[Anonymous No.9872212]

>uses a variable X
>wtf is X
>seriously what the fuck? you just made this up
>scan pages for where X first appears
>it was defined five pages back

[Anonymous No.9872227]

>>9872212

[Anonymous No.9872235]

>consider the possibility that

[Anonymous No.9872237]

>>9872235
I refuse to believe something so disgusting could lie in a math textbook.

[Anonymous No.9872260]

>>9870660
>ought

[Anonymous No.9872284]

>sentence begins with "Then"

[Anonymous No.9872294]

>proof beyond the scope of this textbook

[Anonymous No.9872306]

>I have proved this hypothesis myself but this post is too short to contain it

[Anonymous No.9872315]

>>9870660
don't know what you're moaning about. "assume x to be y" makes it easier for you. possible even.

[Anonymous No.9872373]

>>9870678
LOL is this the same guy? Who is he i saw him on bodybuilding com. He looks schizophrenic

[Anonymous No.9872379]

>>9872373
His curl > his bench

[Anonymous No.9872476]

>The proof of which is trivial, and is left as an exercise for the reader.

[Anonymous No.9872605]

>>9872373
why does he look part black in one pic but not the other?

[Anonymous No.9872624]

>A function is like a machine

[Anonymous No.9872634]

I don't get this fucking meme. What the fuck are the mathematicians supposed to do if not assume and suppose?!

"Let's consider this analytic function, which I found grazing around my back yard. It's fully tangible as a physical entity as are these dicks in my mouth..." Is that what you fucking want? Why not also claim that mathematics were discovered instead of invented while you're at it.

I swear these empiricists are shitting the place up one smug anime face at a time

[Anonymous No.9872689]

>>9872634
>consider

[Anonymous No.9872694]

>>9872624
>it takes one input and spits out one output

[Anonymous No.9872704]

>>9872634
>I

[Anonymous No.9872728]

>>9872624
>it takes one input and shits out one output

[Anonymous No.9872746]

>proof: left as an exercise for the reader

[Anonymous No.9872749]

>>9872728
>>9872694
>>9872624
What's wrong with saying that

[Anonymous No.9872779]

>one-to-one correspondence

[Anonymous No.9872809]

>>9872779
God, I love the look on her face. Imagine slapping her after she glares at you like that, making her cry and squirm, hitting her so hard her lip bursts and starts bleeding! I am so hard right now.

[Anonymous No.9872842]

>>9872809

[Anonymous No.9872882]

>>9872373
he's the (literal) autist that got bullied and slapped by rich piana

[Anonymous No.9872900]

>>9872882
Friendly reminder Rich was in the wrong

[Anonymous No.9872906]

>>9870660
>>9870686
>>9870689
>>9870707
>>9870713
>>9870718
>>9871198
>>9871608
>>9871642
>>9871699
>>9871709
>>9871723
>>9871976
>>9872284
>>9872779
>>9872809
Eradication required.

[Anonymous No.9872999]

>>9872900
Friendly reminder that Rich didn't die, he just left humanity behind like he said he would.

[Anonymous No.9873033]

>>9872906
Suck my cock faggot.

[Anonymous No.9873159]

>>9872999
You aren't wrong there lol

[Anonymous No.9873186]

>>9873033
He's right, though. Literally /v/-tier garbage.

[Anonymous No.9873215]

>>9871666
>(why?)

[Anonymous No.9873236]

>>9871723
If you can't understand what a mapping is then what are you even good for

[Anonymous No.9873244]

>>9872749
A function isn't a machine that cranks out numbers, it's just a map between sets.

[Anonymous No.9873246]

>>9872906
>hey look I replied to everyone’s post, now what?

[Anonymous No.9873458]

[Anonymous No.9873508]

>the solution is left as an exercise

[Anonymous No.9873528]

>>9871666
That's how problems in books start

[Anonymous No.9873581]

>>9873528
no, it's how proofs start

[Anonymous No.9873599]

>>9872624
>>9872694
>>9872728
kek that is my verbatim explanation to retard highschoolers i tutor

[Anonymous No.9873680]

Fucking sophistry

[Anonymous No.9873684]

>>9871198
>using 'without' as in the antonym of 'within'
also fuck you whence is great

[Anonymous No.9873690]

>>9872634
Proof should be written as lambda functions taking variables/assumptions as inputs.

[Anonymous No.9873693]

>by the axiom of choice

[Anonymous No.9873707]

>>9873693
That one's great, axioms are literally a cop-out.
>can't be proved so here's a get out of proof free card

[Anonymous No.9873736]

>>9872634
>Let's consider

[Anonymous No.9873741]

>>9872809
>beating wemen
Calm down Mohammad.

[Anonymous No.9874089]

>>9872842
>>9873741
>t. beta losers

[Anonymous No.9874095]

>>9873707
Is this bait? You can't prove anything at all without some set of axioms and logical foundations. In fact you classify results according to the "strength" of the axioms required to obtain them. Debate about whether a given axiom is "right" or "wrong" is absurd

[Anonymous No.9874125]

>>9874095
>You can't prove anything at all without some set of axioms and logical foundation
Prove this

[Anonymous No.9874134]

>>9874125
Trivial

[Anonymous No.9874313]

>Lets pretend that

[Anonymous No.9874987]

>>9873690
is this lean?

[Anonymous No.9875169]

>>9872634
>Why not also claim that mathematics were discovered instead of invented while you're at it

[Anonymous No.9875281]

>>9873236
if you can't understand what the point of this thread is then what are you even good for

[Anonymous No.9875282]

show that

[Anonymous No.9875285]

observe

[Anonymous No.9875289]

>>9872694
>>9872728
Well? Do they spit or shit?

[Anonymous No.9875299]

>Andrew
>Betty
>Chris

[Anonymous No.9876044]

>>9874987
Yeah.

[Anonymous No.9876134]

>>9873528
Yeah, so?

Why ironize about it?

[Anonymous No.9876145]

>>9875299
>Bashir
>Natsuko
>Chin

[Anonymous No.9876670]

>>9876145
>Fatima

[Anonymous No.9876701]

In reality

[Anonymous No.9877021]

>>9876044
kek do you go to cmu? last I checked version 2 was not worked on anymore, which was interesting since it supported hott. Don't know what they're up to with v3. What does it buy you over coq/agda?

[Anonymous No.9877068]

>IMAGINE

[Anonymous No.9877091]

>proof: Exactly like the one 4 chapters ago with some modifications

[Anonymous No.9878725]

>>9877021
Nah, ANU.

I've never used coq/ada so I'm not sure. I only learnt of it from v3.
The thing lean devs always shill is the ability to write automation in lean itself rather than a metalanguage.
I don't know how it compares to other languages but there is a fairly active development scene (both the language and the math library).
I also think the syntax and interface (with the visual code extension) are pretty nice.

[Anonymous No.9879156]

>>9878725
cool mate, that's hella far. Agree that the term language is better than coq, from what little I saw. i still think current proof assistants are too rigid. Working a coq project right now, pretty draining. Type systems are nice, but not flexible/automated enough (even for someone in pl and swears by pfpl). Optimistic about the future tho, maybe with hott and the right tools we can get much more convenient equality/equivalences for programming.

[Anonymous No.9879322]

>without loss of generality

[Anonymous No.9879959]

>Estimate as necessary

[Anonymous No.9880025]

>>9870660
>where

[Anonymous No.9880044]

>Set

[Anonymous No.9880050]

>>9879322
This one's great. You literally don't have to do half the work. WLOG baby.

[Anonymous No.9880055]

>by analogy

[Anonymous No.9880101]

>>9870660
>What if

[Anonymous No.9880154]

>>9879156
Yeah writing code is pretty slow for me. You basically need to know the names of every relevant lemma. Makes you realise how many small logical steps we make without even thinking about.
What are you doing in coq if you don't mind me asking?
I don't actually know a lot about hott but I've been planning to read the book for a while now.
I'm optimistic for the future too. I think human readable proofs are another import step that aren't really cared about enough though.

[Anonymous No.9880224]

>Normal mathematics

[Anonymous No.9880303]

>>9880224
>in ZFC

[Anonymous No.9880767]

>>9872749
There functions which are not 1:1.
>Consider
f(x)=x^2. Inputting values -2 and 2 both result in 4, this is a many to one form of function.

[Anonymous No.9880807]

>>9880767
"Takes in one input and spits out one output" does not mean "injective."
The actual problem with the phrase is that it's not rigorous

[Anonymous No.9882460]

>>9880154
long story short, I'm currently designing a dsl for generic programming, specifically we need to support enumeration. Started with coq thinking we can prove correctness/exhaustiveness of the enumeration, but the way I approached it (embedding of gallina into the dsl) turned into a clusterfuck and in the end couldn't support all the features. Literally just downloaded agda since I wanted to use induction-recursion to define a universe with expressive types. Kinda bummed that coq didn't work out, but pretty excited about the new approach. Might even look into HIT to deal with symmetry.

Yeah readable proofs aren't really focused on. This is especially the case for coq, since tactics is the main way of proving theorems. It really is "write-only". I honestly can't understand anything I write unless I go through each step in the ide.

The situation for raw proof terms aren't too good either. Dependent terms get complex and hard to read very quickly.

However, if you just need to read the theorem at the end of the day, it isn't so bad.

[Anonymous No.9883795]

>>9876670
>John
>Paul
>George
>Ringo
>The Walrus

[Sage No.9883867]

>>9871642
Lurk more or go back to rebbit

[Anonymous No.9883987]

>>9877091
I did this

[Anonymous No.9884166]

>>9873741
Based Mohammad

[Anonymous No.9884249]

>>9871748
>tell someone to lurk more
>never explain it

[Anonymous No.9884286]

>>9884249
If you don’t get it, you shouldn’t be on this board

[Anonymous No.9884298]

>Draw picture of mathematical concepts

[Anonymous No.9884441]

>lets suppose we assume that f(x) is a function

[Anonymous No.9885469]

>>9872167
Kek

[Anonymous No.9885691]

>by inspection

[Anonymous No.9885771]

>>9870811
>thus
>therefore
>as such