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Logic cw help by Martha Trotwater - Thu, 11 Dec 2014 16:07:45 EST ID:FYItrjmk No.14517 Ignore Report Reply Quick Reply
File: 1418332065440.jpg -(33613B / 32.83KB, 420x319) Thumbnail displayed, click image for full size. 33613
Hey if anybody could take a look at this and give me the answers and or help me understand whats expected.
Suppose you are given an algorithm R that can test for any propositional
formula in Conjunctive Normal Form whether it has a resolution refutation or not.
(a) Describe (informally) how to construct from the algorithm R an algorithm T that can
test for any propositional formula in Disjunctive Normal Form whether it a tautology
or not.
(b) Demonstrate how your algorithm T works using the DNF
A ∨ (¬A ∧ B ∧ ¬C) ∨ (¬A ∧ ¬B ∧ ¬C) ∨ (¬A ∧ C)
(c) Explain how the computational complexities of the algorithms R and T related?

How to formalize this? by Emma Secklebury - Sat, 25 Oct 2014 08:42:51 EST ID:8Yw0Br5B No.14438 Ignore Report Reply Quick Reply
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How to mathematically formalize that the belief in God is absurd because there are infinitely many "supernatural" beings that can exist, and God is just one of them, and that THERE ARE INFINITELY MANY BEINGS WHICH EXCLUDE GOD'S EXISTENCE out of possibility. Ex: Out of invisible flying goblins, invisible pink unicorns, invisible demon alien reptiles, etc.
15 posts and 2 images omitted. Click Reply to view.
Lydia Gimmlehall - Tue, 09 Dec 2014 11:09:31 EST ID:Dk8yywxc No.14508 Ignore Report Quick Reply

Well, many of the theories have their basis and motivation rooted in empirical observation
Cornelius Bummlenud - Thu, 11 Dec 2014 13:05:48 EST ID:L5NP4VLn No.14515 Ignore Report Quick Reply
What's God?
Fanny Snoddale - Thu, 11 Dec 2014 13:23:45 EST ID:dL8jDLUE No.14516 Ignore Report Quick Reply
1418322225184.jpg -(25743B / 25.14KB, 990x233) Thumbnail displayed, click image for full size.
God is mathematics. Resurrecting itself through our application of it in technology.
NJ... Where art thou?
Edwin Hattingworth - Wed, 03 Jun 2015 15:39:16 EST ID:4aRbvkOu No.14774 Ignore Report Quick Reply
Mathematics is built on Aristotelian first-order logic, using Zermelo-Fraenkel Set Theory (along with the Axiom of Choice). The axioms of mathematics are *chosen* so that the natural numbers (i.e. the counting numbers) can be constructed logically, step-by-step, and end up with all the usual properties we expect natural numbers to have. Yes, it is "all theory," but that theory is rooted heavily in elementary observations we make about quantity and measurement.

While there are a few mathematicians who look at other axioms for the basis of their mathematical system (dropping the axiom of choice, for instance), even these don't stray far from the general intuition we expect from counting. Don't even get me started on how COMPLETELY unrelated mathematics and metaphysics are: math is *not* number-wizardry.
William Drenkingold - Thu, 01 Dec 2016 03:46:14 EST ID:I4oaqfW8 No.15282 Ignore Report Quick Reply
Psssssssssst. Here's something I understood when I was 17.

> Infinite exclusive gods can be thought of
> => probability of one of them existing is an infinitesimal

> Infinite non-exclusive gods can be though of
> => probability of any such god existing is 50%

It's really not that hard, folks.

Theta by Samuel Clissleridge - Thu, 11 Dec 2014 00:07:47 EST ID:zBSUDYOt No.14511 Ignore Report Reply Quick Reply
File: 1418274467054.png -(5718B / 5.58KB, 302x450) Thumbnail displayed, click image for full size. 5718
I'm currently trying to relearn some math skills that became a little blurry over the years so I can make the transition back into college a little bit easier, I'm using Khanacademy as my guide and I'm having trouble with trigonometry or with them?

So on the site I can't ever tell what angle I'm supposed to be solving for since there is no theta symbol. For example it gives me the following parameters: cos(<ABC) AC=12, BC=16, AB=20. I'll also make a diagram on MS paint showing exactly as the site does.

With the information listed above I'd assume theta would be at angle A because its Triangle ABC and not BAC, is my assumption correct? Can someone help me understand which angle I should use as my prospective so I can get the correct adjacent and opposites angles.
Samuel Clissleridge - Thu, 11 Dec 2014 00:56:07 EST ID:zBSUDYOt No.14512 Ignore Report Quick Reply
Yeah If a mod can just kill this post that'd be great I figured it out, plus it was asking for an angle and not triangle(misinterpreted the symbol) so that was part of the confusion, thanks.

What kind of graph is this? by Polly Wammlelock - Mon, 01 Dec 2014 06:14:44 EST ID:pok0PfIZ No.14500 Ignore Report Reply Quick Reply
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Weird question I know, but I'm really high and this thing is reading like a fucking fractal

%Wasn't quite sure where to post this, apologies if I'm on the wrong board%
Lydia Parringhall - Mon, 01 Dec 2014 12:22:59 EST ID:L5NP4VLn No.14501 Ignore Report Quick Reply
It's a Venn diagram
Doesn't look very fractal really..
Lydia Blondlemudge - Thu, 04 Dec 2014 07:43:36 EST ID:ZfGYcL4C No.14502 Ignore Report Quick Reply

It did to me at the time I like it though

Clearly I need to review something... by user - Wed, 26 Nov 2014 17:42:16 EST ID:RzQObfiO No.14496 Ignore Report Reply Quick Reply
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Can someone explain this to me? It seems like I do not understand factoring at all.

I have no idea how x = 0, 3, and -2.

Thanks in advance.
Angus Nenkinson - Wed, 26 Nov 2014 21:50:46 EST ID:LS/jID0L No.14497 Ignore Report Quick Reply
Cornelius Summernedge - Thu, 27 Nov 2014 04:04:42 EST ID:RzQObfiO No.14498 Ignore Report Quick Reply
Thanks, I'll use this from now on.

Math essay by Doris Chabblesadge - Fri, 17 Oct 2014 15:57:47 EST ID:GWtHalR/ No.14416 Ignore Report Reply Quick Reply
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I'm taking a forced module that requires you to write an essay and do a presentation on a topic in math that isn't normally covered in the standard syllabus. For the essay you basically need to rewrite a chapter of a text book including theorems, proofs, examples, diagrams etc.

Could anyone recommend some interesting topics? Some topics that people have done in the past are:

-rubik's cubes and group theory
-p-adic numbers
-set theory and axiom of choice
-hilbert spaces
-algebraic curves
-queuing systems

I'm in my second year so it can't be a topic that's too difficult to understand.
3 posts omitted. Click Reply to view.
Shit Gabblemug - Sat, 25 Oct 2014 15:55:16 EST ID:GWtHalR/ No.14440 Ignore Report Quick Reply
Thank you for this
Jarvis Blimmerhall - Tue, 28 Oct 2014 18:44:58 EST ID:1xiHvl+b No.14454 Ignore Report Quick Reply
"In one sense, there are twice as many numbers between 0 and 2 as there are between 0 and 1 (because 0 to 2 is twice as "long" as 0 to 1); but in another sense there are exactly the same number of numbers between 0 and 2 as there are between 0 and 1.

>[Undefined, grammatical filler] there are twice as many numbers between 0 and 2 as there are between 0 and 1
>[Undefined, grammatical filler] there are exactly the same number of numbers between 0 and 2 as there are between 0 and 1.

"This is beginning to approach the level of comfort you need with the quirks of infinite collections of numbers to understand the Banach-Tarski theorem. If you're not quite comfortable with this so far, please go back and reread before continuing on. "

you shouldn't have
Cornelius Blackwater - Tue, 28 Oct 2014 21:04:48 EST ID:EsiytcUg No.14455 Ignore Report Quick Reply
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Check out Ramsey theory, it's about inveitable structures, pretty juicy stuff philosophically. "Total disorder is impossible". It's one of those lovely areas that have problems that are (relatively, given a certain audience) simple to formulate but difficult to solve.

"Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack." - Erdos
Edward Wodgebanks - Tue, 18 Nov 2014 03:09:28 EST ID:pAQz9OgX No.14492 Ignore Report Quick Reply
ooo ooo ooo non-standard analysis
Lillian Demmlepodge - Fri, 21 Nov 2014 06:56:16 EST ID:GWtHalR/ No.14493 Ignore Report Quick Reply
Good idea but unfortunately we've already covered it in a combinatorics module. My lecturer used that quote too :)

I'll look into it. Good topic too as I could present the criticisms against it too.

sound synthesis by Jarvis Huddlefuck - Mon, 17 Nov 2014 08:55:10 EST ID:RJugJy5x No.14488 Ignore Report Reply Quick Reply
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So, I put this in music and production seing as its sound synthesis but the mods locked the thread so will try here..

can ANYONE help with these questions? any input appreciated.
Jarvis Fuckletire - Mon, 17 Nov 2014 18:56:03 EST ID:d/+G3sr/ No.14489 Ignore Report Quick Reply
frequency modulation

Wc = carrier frequency; i = modulation index; Wm = modulation frequency
Faggy Pinkinhick - Mon, 17 Nov 2014 22:32:49 EST ID:sVDeU0lu No.14490 Ignore Report Quick Reply
I don't know what's up with that mod, seemed like it belonged in /m/. It's called music & production board after all.
Charles Geblingworth - Mon, 17 Nov 2014 23:01:06 EST ID:bccTK08l No.14491 Ignore Report Quick Reply

thankyou friend, it is appreciated

Is this a problem? by Clara Chisslesore - Sun, 19 Oct 2014 21:54:03 EST ID:IJ85y6zt No.14423 Ignore Report Reply Quick Reply
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Is it a problem that set theory is based on mathematical logic, whereas mathematical logic is based on set theory? If so, why?
4 posts and 1 images omitted. Click Reply to view.
Polly Dambleville - Mon, 27 Oct 2014 20:56:01 EST ID:jEbtLayo No.14452 Ignore Report Quick Reply
I think he's referring to the fact that in order to define truth in first order logic you have to use structures, which are sets equipped with functions and relations. You need to know how these things work in order to set up FOL but in order to formalize sets you need FOL.
Edward Cuzzlehall - Sat, 01 Nov 2014 13:25:09 EST ID:Dk8yywxc No.14461 Ignore Report Quick Reply

A first order theory doesn't have a truth function. A first order theory has axioms, rules of deduction, and a language to express it in. There are no sets, only names that are being manipulated using rules, and the resulting theorems. Of course you can talk about a model (structure) for a first order logic where you can have sets and a truth function but the theory itself is more fundamental and acts as a building block.

It's confusing because when you come up with a theory, you intuitively have in mind what the theory means, i/e you already have a structure in mind. So if I'm talking about the theory of natural numbers then 1=1 is valid (true in every structure), but when you separate the theory from the structure 1=1 is only a theorem, there is no notion of true or false. In a theory you only have the starting place and the theorems that result from it. 1=1 here isn't a statement about numbers, it is just symbols that are neither true or false, we just got it from manipulating some symbols that we started with.

I should mention that there is already the idea of a functions and predicates within the language, but there is formally not a truth function until you have a model. You do, however, need some set theoretic notions to begin talking about structures and models as you mentioned. But it is really basic stuff that doesn't seem to be problematic in this case, questions like "what is a set". My main point though is that a first order theory doesn't need set theory. Set theory needs the first order theory, while structures and models need (basic) set theory.
Phoebe Turveyspear - Tue, 04 Nov 2014 02:03:56 EST ID:jEbtLayo No.14465 Ignore Report Quick Reply
If you take deductive systems as your primitive constructions then you can construct set theory without ever referring to sets. The only problem here is that you can't have any notion of soundness or completeness until you define some notion of truth. I see what you're saying though, usually it's taught by defining truth first and then talking about deductive systems which never quite sat well with me since you had to use sets/functions/relations and all of that stuff without ever formally defining them.
Hamilton Buddlemack - Wed, 05 Nov 2014 12:24:47 EST ID:Dk8yywxc No.14466 Ignore Report Quick Reply

Completeness can be interpreted as meaning for every formula A, you either have A or -A as a theorem, i/e every formula A is decidable. You don't quite need truth to do that. You're right about soundness though, it refers to the validity of a formula, which is a statement about models essentially. Can't have models without sets.
Molly Goodgold - Sat, 08 Nov 2014 21:47:13 EST ID:jEbtLayo No.14471 Ignore Report Quick Reply
I meant completeness in the sense that every true statement in first order logic is deducible. http://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem
They really need to have another name for this.

How to Break Even + Profit on boxed software? by Yaranaika - Tue, 12 Aug 2014 14:20:06 EST ID:8ADnuosf No.14279 Ignore Report Reply Quick Reply
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Ok, say a piece of software in a boxed copy is $150 solid.

To break even would be to make $150 back on every copy correct?

To profit slightly without being accused of scalping would be maybe $50 on the original price? (I'm selling these at an anime convention, so I need to pay off my table and eat too...)

I've sold goods at 200% Markup last year but these are more physical and mystically rare items like certain foods, unlocked import phones from Japan...etc
Angus Brirringkadge - Thu, 06 Nov 2014 14:24:24 EST ID:REpT3xaI No.14467 Ignore Report Quick Reply
1) How much money do you need to make to cover expenses and your investment? 2) How many units do you expect to sell?
Cut the second number into a third and divide that into the first number. (#1)/(#2/3)

That's your reasonable markup price

Discrete Math and Counting by Martin Chashway - Tue, 21 Oct 2014 01:39:18 EST ID:vbQtHDF1 No.14432 Ignore Report Reply Quick Reply
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Hi /math/, I've got a question regarding counting in Discrete Mathematics. The textbook I have, "Discrete Mathematics With Ducks," is truly garbage and not helpful at all when it comes to... anything. http://www.amazon.com/product-reviews/1466504994/ref=acr_dpx_hist_1?ie=UTF8&filterBy=addOneStar&showViewpoints=0

The question I'm on asks:
How many positive integers solutions are there to the equation y1 + y2 + y3 + y4 + y5 + y6 = 13?

I need some help with this. After break I'm a bit lost. This is under the section of Combinatorial problems, and we've been using the Principle of Inclusion and Exclusion as well as this "stars and bars" technique (I'm not sure if anyone is familiar with this, it might just be my god-awful textbook). So ideally the problem could be solved that way. Thanks.
Esther Sengerford - Tue, 21 Oct 2014 10:52:03 EST ID:Dk8yywxc No.14433 Ignore Report Quick Reply

I don't know about stars and bars but here is how I would think about this.

This problem is like trying to put 13 balls into 6 boxes with at least one ball in each box. Put a ball in each box, so there are 13-6= 7 balls remaining. You can distribute the remaining 7 in C(7+6-1,7)=C(12,7)=792 different ways to do it. The reason there is a -1 is because we don't want 0 to be included.
Basil Gesslepark - Fri, 31 Oct 2014 19:17:48 EST ID:dJKFjM4J No.14460 Ignore Report Quick Reply
Stars and bars? Just imagine a whole bunch of numbered blocks, 1 .. N. You wrote down 5 plus signs. We're going to remove 5 blocks from the N. This will allow removing 5 consecutive from the left, that's okay for now. The spacing between the blocks indicates the grouping of the integers (so an island of 5 blocks: y_k = 5). The only trouble is you specified positive integers, so we should eliminate all the solutions containing 0.

First, how big is N? N should allow for 13 blocks after removing 5, so N = 18.

So the answer is less than (18 5).

Instead of adding up to 13, we could just distribute a 1 to each y_k and add up to 13 - 6 = 7. So (7 5) would represent all the ways to introduce splits in the remaining 7 numbered blocks to distribute them uniquely to y1..y6.

(7 5) = 42, so the answer is 42? It's either 792 or 42, who knows.

Refreshing math knowledge. by Ian Tootson - Wed, 29 Oct 2014 11:54:18 EST ID:GCILLCAz No.14456 Ignore Report Reply Quick Reply
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I'm a undergraduate math major who has been out of college for about 2 years. I want to go back to uni but I am extremely rust on my higher level math skills. What tools or resources could I use to revive my mathematics knowledge? This is where my poor note taking has taken its toll.
Should I just use math GRE subject test practice books or do you know of any thing that will help. I am not looking to relearn like kahn academy just practice tests for calculus, linear algebra, multuvariate, and complex.
Thomas Bepperkit - Thu, 30 Oct 2014 11:54:13 EST ID:Dk8yywxc No.14458 Ignore Report Quick Reply

If you don't remember it and aren't taking classes yet, buy some positively reviewed textbooks. Work through them and do some exercises too. Don't forget to do a couple of exercises!

A little bit of google searching should find you some books that people generally regard as good. Don't worry if you work through them slowly, just keep at it every day.
Alice Bardwill - Fri, 31 Oct 2014 12:07:00 EST ID:Ov5dnuCH No.14459 Ignore Report Quick Reply
For calculus just pirate a copy of the Stewart textbook and go through it. It's your standard plug n chug textbook and a huge number of universities use it so it'll put you in good stead for when you're finally back. If you get stuck you can always supplement with the internet. It goes all the way up to multivariable calc, vector calc etc.

Same for linear algebra really. The book we use is "Linear Algebra - A Modern Introduction". Again it can be pirated online.

How do I prove this? by Edward Lightford - Sun, 26 Oct 2014 11:49:57 EST ID:BH6DA7ss No.14443 Ignore Report Reply Quick Reply
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Can anybody help me with this problem?

let f(n)= sum (from i=2 to n) 1/(i ln(i)
Show that f(n) = Θ(ln(ln(n))
Edwin Brocklewell - Tue, 11 Nov 2014 13:41:05 EST ID:qABD7ibX No.14477 Ignore Report Quick Reply
∑1/(i*ln(i)) ≃ ∫dx/(x*ln(x)) = ∫1/x 1/ln(x) dx
Let u=ln(x), du=dx/x
∫ 1/u du = ln(u) = ln( ln(x) )

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