doogly wrote:This stinks like something with a two line proof using categories.

Obligatory reference

- Fri Feb 23, 2018 11:24 am UTC
- Forum: Mathematics
- Topic: Prove that dim Spec A = dim Spec A/p + dim Spec A_p
- Replies:
**2** - Views:
**428**

- Wed Feb 07, 2018 7:01 pm UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9841** - Views:
**1658218**

Assuming this is the global object( window or global ): (function() { function factorial(n) { // or any function such that f(0)=f(1) and f(2)/=f(3) let res = 1; for(let i = 2; i <= n; ++i) res *= i; return res; } let something = 4; Object.defineProperty(this, 'a', { get() { let res = factorial(somet...

- Thu Dec 14, 2017 4:16 pm UTC
- Forum: Mathematics
- Topic: Bump Function
- Replies:
**7** - Views:
**1673**

This may or may not be useful: by simply taking the derivative, we get that f'(x) = f(x) * g 1 (x) (for some g 1 ) therefore f''(x) = f'(x) * g 1 (x) + f(x) * g 1 '(x) = f(x) * (g 1 (x))^(2) + f(x) * g 1 '(x) = f(x) * g 2 (x) (for some g 2 ) This can be extended to f (n) (x) = f(x) * g n (x)...

- Thu Oct 05, 2017 12:44 pm UTC
- Forum: Mathematics
- Topic: What is linear algebra?
- Replies:
**3** - Views:
**1174**

Linear algebra is less about "lines and their equals" and more about vector spaces, and linear functions between them. Linear functions are functions that preserve vector addition and multiplication by a scalar. In linear algebra you'll learn what a vector space is, and you'll learn about ...

- Mon Sep 18, 2017 9:52 pm UTC
- Forum: Coding
- Topic: Manufactoria - Make Turing Machines with Conveyor Belts
- Replies:
**350** - Views:
**82356**

Looks cool from the video, and it has a demo so I can check it out when I get home! Excellent, let me know how it goes! Nice interface, although I could've gone with a smaller font size. I like that you added keybinding for the different modules, however I would like the ability to rebind keys(for ...

- Mon Sep 18, 2017 5:04 pm UTC
- Forum: Coding
- Topic: Manufactoria - Make Turing Machines with Conveyor Belts
- Replies:
**350** - Views:
**82356**

I'm going to be incredibly rude and necro this 7-year-old thread to post some news: I've made a new game! It's called Silicon Zeroes, it's a spiritual sequel to Manufactoria, and it's out right now on Steam and itch.io. Just a heads-up :) Looks cool from the video, and it has a demo so I can check ...

- Tue Sep 12, 2017 10:21 pm UTC
- Forum: Logic Puzzles
- Topic: 538 hats riddle
- Replies:
**20** - Views:
**2927**

That solution reminds me of another riddle, where each of n participants is given a hat with a random color out one of n different colors(and what color one person gets is independent of what the rest get) and they need to form a strategy such that at least one of them must guess their own color cor...

- Tue Sep 12, 2017 5:06 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9841** - Views:
**1658218**

Indeed it appears that none of Internet Explorer, Edge, and IE Mobile support the 'tab-size' CSS property, at least according to MDN's documentation.

I guess Microsoft really want you to use a very specific tab-size, or else...

I guess Microsoft really want you to use a very specific tab-size, or else...

- Tue Aug 08, 2017 10:42 pm UTC
- Forum: Coding
- Topic: var == 'value' vs 'value' == var
- Replies:
**20** - Views:
**6142**

Yeah, that's a reasonable retort. Anyone who does "foo() == true" is making a mistake in the first place. ^_^ I've seen that used in C# where foo() returns (bool?) as shorthand for: bool? x = foo(); if(x != null && x.Value) // ... or bool? x = foo(); if(x.HasValue && x.Val...

- Sat Jul 15, 2017 9:19 pm UTC
- Forum: Logic Puzzles
- Topic: New kind of puzzle
- Replies:
**17** - Views:
**2732**

I can do it for you if it just come to the colors inside the circles (It will take me 30 minutes) but how could I replace the links (in yellow) between circles? After rethinking I believe that it will hard to guess the rules. So if no one find the rules (which is part of the puzzle) then I will pos...

- Sat Jul 15, 2017 8:41 pm UTC
- Forum: Logic Puzzles
- Topic: New kind of puzzle
- Replies:
**17** - Views:
**2732**

Looks interesting, but I'm having trouble with the colors(I have color-vision deficiency), do you have a version where the colors are replaced by numbers/letters?

- Thu Jun 29, 2017 11:13 am UTC
- Forum: Religious Wars
- Topic: Spaces in paths & filenames
- Replies:
**45** - Views:
**6172**

Does DOS/Windows allow single quotes at all? I seem to remember it only liking double quotes, and wine cmd says "File not found" when I try to use single quotes with dir and type. Testing on a windows 10 machine: cmd.exe doesn't accept 'single quotes', only "double quotes". powe...

- Sun Jun 25, 2017 3:52 am UTC
- Forum: Religious Wars
- Topic: Spaces in paths & filenames
- Replies:
**45** - Views:
**6172**

Funnily enough, Powershell handles tab-completion with files that have spaces in them just fine, it even automatically wraps the path in double quotes for you. Powetshell is far from perfect, but at least you can easily type /pro[tab, perhaps more than once] to get "C:\Program Files (x86)\"...

- Wed Jun 14, 2017 5:01 am UTC
- Forum: Mathematics
- Topic: What would happen if $-1 bills were minted?
- Replies:
**20** - Views:
**4526**

Something like that exists here in Norway [...]A giro: I buy something from you, you write a giro and give it to me. I hand in the giro to my bank, and the money moves from my bank to yours. What if you don't hand the giro to the bank? Jose I'd assume it'd result in either a lawsuit, or in the loss...

- Tue Jun 06, 2017 8:10 pm UTC
- Forum: Logic Puzzles
- Topic: Guess the Pattern
- Replies:
**21** - Views:
**4294**

Keeping a list of my observations so far. ⋅ All shown outputs are prime or X ⋅ All shown outputs, where they are not X, are coprime to the inputs. ⋅ All integers of the form 6n+1 shown, except for 1, result in X ⋅ All other shown integers that result in X ...

- Thu May 25, 2017 2:11 pm UTC
- Forum: Mathematics
- Topic: How to learn about radical expressions and equations ?
- Replies:
**12** - Views:
**2587**

A bit more information about your current mathematical education would be helpful for us to guide you in the correct direction.

- Tue May 23, 2017 11:37 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9841** - Views:
**1658218**

Even better. As you guessed, Javascript will automatically add a semicolon at the end of a line if it makes syntactic sense. But then the brace becomes the start of a block statement, not the start of an object literal. Inside that block is the (useless) label "foo", on the (pointless) st...

- Tue May 23, 2017 9:55 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9841** - Views:
**1658218**

I don't know much javascript but I am guessing line breaks act as statement separators(like semicolon), so the first one acts like return; essentially returning nothing, while the second one has an opening brace so it returns everything until the closing brace. I am guessing that's because javascrip...

- Sat May 06, 2017 10:11 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

Yes, basically. What you want is simply to derive the (n=k+1) case given the (n=k) case, as has been done in the proof you've given, along with a base case.

- Sat May 06, 2017 10:04 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

It's not, it is just missing a base case.

- Wed May 03, 2017 4:42 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

The even/odd definition I posted apply for all integers, not just the positive ones. 0 is a multiple of 2(2*0=0), therefore it is even. 0 is divisible by every number except 0.

- Wed May 03, 2017 4:36 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

Yes! That is a valid argument, and a perfect example of proof by induction. You have the base step, the induction step, and you correctly justify your conclusion using known properties of even and odd numbers. But my argument still contains an assumption that I'd need to build out (I think), which ...

- Wed May 03, 2017 3:57 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

The first sentence you wrote just reiterates the definition of an even number. You gave no justification for why every integer that isn't even to be odd, since odd means 1 greater than an even number. The proof by induction provides such justification. I have to start somewhere. By necessity, becau...

- Wed May 03, 2017 3:28 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

The first sentence you wrote just reiterates the definition of an even number. You gave no justification for why every integer that isn't even to be odd, since odd means 1 greater than an even number. The proof by induction provides such justification.

- Wed May 03, 2017 3:09 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

What background knowledge? Do you have some other proof that every integer is either even or odd? Remember that "n is even" means "there exists m such that n=2m" and "n is odd" means "there exists m such that n=2m+1" Did you ever prove the statement "ever...

- Wed May 03, 2017 2:55 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

:arrow: It's pedagogically useful. It is nice to practice proof by induction if you do not understand induction by using it to prove things which you can already understand and prove by another means. I would agree with that, but the problem with the even-odd example is that it doesn't (at least in ...

- Wed May 03, 2017 2:42 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

Proof by induction is usually useful when you want to prove some statement about all integers greater than or equal to some starting value. The original problem in this thread has the statement "1+2+3+...+(n-1)+n=n(n+1)/2" The even-odd problem has the statement "n is even or n is odd&...

- Wed May 03, 2017 2:25 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

Fun fact: the top answer to the question "how to prove that every integer is either even or odd" on math stackexchange is proof by induction.

https://math.stackexchange.com/question ... ven-or-odd

https://math.stackexchange.com/question ... ven-or-odd

- Wed May 03, 2017 5:21 am UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

I'll just leave this here. It's the post I posted a page ago and was completely ignore by mathdofus. I ask that you read this post, if you hit a point you don't understand, write down what you don't understand on a piece of paper and continue reading, writing the points you don't understand. Then re...

- Wed May 03, 2017 4:17 am UTC
- Forum: Coding
- Topic: Basic Question Involving Functions (Python)
- Replies:
**18** - Views:
**5201**

The tutorials and books Xanthir linked are aimed at people who have no programming backgroud, so they should teach you, along with the specifics of the python language, how programming works. I didn't check them all but they probably include example problems and solutions(using python). Once you hav...

- Tue May 02, 2017 9:49 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

But you don't seem to know how to prove them, which is what we're doing here. We keep circling around this same problem. The induction step is just a conditional proof. If I demonstrate that a base case is true, and then demonstrate that if the k case is true then the (k + 1) case is true, then I'v...

- Tue May 02, 2017 9:00 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**18432**

It's a proof by induction of the statement "every natural number n is either even or odd" Another, simpler(and pretty trivial) proof by induction would be "every positive natural number n is divisible by 1" To prove that by induction, we follow the basic steps of induction: Base ...

- Mon May 01, 2017 4:12 pm UTC
- Forum: Coding
- Topic: Basic Question Involving Functions (Python)
- Replies:
**18** - Views:
**5201**

While I am not too well versed in python, I think it is better for you to think about these functions as procedures, or subroutines, basically they are there to divide up your code and eliminate a lot of rewriting code. Some languages allow passing functions as arguments to other functions, which ma...

- Fri Apr 21, 2017 6:12 pm UTC
- Forum: Language/Linguistics
- Topic: Miscellaneous language questions
- Replies:
**535** - Views:
**60108**

I'd say yes because we don't have a year zero, thus years 1-10 form a decade

- Fri Apr 21, 2017 1:54 pm UTC
- Forum: Mathematics
- Topic: i want to learn factoring polynomial equation
- Replies:
**23** - Views:
**3566**

doogly wrote:It also helps to practice polynomial long division. Like, what is 2x^3 + 3x^2 - x - 2 / x - 4 ?

That would be 2x^3 + 3x^2 - x - 2x^(-1) - 4

- Mon Apr 17, 2017 9:15 pm UTC
- Forum: Mathematics
- Topic: Qustion about 3D
- Replies:
**3** - Views:
**1549**

Flumble wrote:(x' = y' = 0 is trivial, so I'll assume it's not considered)

x' = tanh(x+1)*y*z+1.37+(x+z)*ln(1+x^2+y^2+z^2)

y' = tanh(x)*z-cos(z+x)*y

I dare you to give a better projection.

Please show how this projects the Utah teapot

- Fri Apr 14, 2017 6:59 pm UTC
- Forum: Religious Wars
- Topic: What is log² x?
- Replies:
**11** - Views:
**4027**

Well, a bigger ∘ fits with union and intersection notation, and I believe ∘ is closer to sets than to numbers. I also recall seeing + and × used instead of the sigma and pi somewhere - oh right it was a Youtube video talking about notation...

- Fri Apr 14, 2017 12:04 am UTC
- Forum: Religious Wars
- Topic: What is log² x?
- Replies:
**11** - Views:
**4027**

I'd write (log ∘ log)(x), and for variable(or large) function application, something like (o n log)(x) and maybe for a given sequence of functions (f m ,f m+1 ,f m+2 ...,f n-1 ,f n ), I'd write something like ( i=m o n f i )(x), similar to sigma notation and pi notation for sums and products, the ma...

- Wed Apr 12, 2017 8:06 pm UTC
- Forum: Computer Science
- Topic: Favorite Programming Language
- Replies:
**16** - Views:
**6849**

So far, every language I met had *some* use case where it shines, and *some* use case where it's a poor choice. What was Java's "shining" example? *runs* C#. I prefer Haskell tho. Hell, when I need a quick calculation(read: wait, what was sin (exp 3.12) again? Ah, right -0.61...), I just ...

- Wed Feb 22, 2017 1:35 pm UTC
- Forum: Mathematics
- Topic: Convert points from a 2d space with a real dimension x and an imaginary dimension y
- Replies:
**19** - Views:
**3212**

I'm not going to go and do a full Treatid on this issue [offtopic] This became a thing, now it's time to spread it in 4chan so everyone would use it without knowing what the hell it is. [/offtopic] MrY, are you looking for a transformation T from R^(2) to R^(2) such that for any pair of points x an...