## Search found 197 matches

- Wed Jun 14, 2017 5:01 am UTC
- Forum: Mathematics
- Topic: What would happen if $-1 bills were minted?
- Replies:
**20** - Views:
**1307**

### Re: What would happen if $-1 bills were minted?

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:
**1008**

### Re: Guess the Pattern

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:
**508**

### Re: How to learn about rational expressions and equations ?

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:
**9676** - Views:
**1426997**

### Re: Coding: Fleeting Thoughts

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:
**9676** - Views:
**1426997**

### Re: Coding: Fleeting Thoughts

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

: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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**16** - Views:
**1983**

### Re: Basic Question Involving Functions (Python)

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**252** - Views:
**4149**

### Re: Mathematical Induction - Introductory Question

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:
**16** - Views:
**1983**

### Re: Basic Question Involving Functions (Python)

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:
**361** - Views:
**25366**

### Re: Miscellaneous language questions

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:
**1301**

### Re: i want to learn factoring polynomial equation

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:
**533**

### Re: Qustion about 3D

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:
**1395**

### Re: What is log² x?

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:
**1395**

### Re: What is log² x?

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:
**13** - Views:
**2633**

### Re: Favorite Programming Language

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:
**1649**

### Re: Convert points from a 2d space with a real dimension x and an imaginary dimension y

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...

- Wed Jan 18, 2017 1:57 pm UTC
- Forum: Logic Puzzles
- Topic: New puzzle : Equalize
- Replies:
**13** - Views:
**1937**

### Re: New puzzle : Equalize

Another "random" setup that doesn't have a unique solution:

As it has at least 2 solutions:

Code: Select all

` `

bb

r r

b b

rr

As it has at least 2 solutions:

Code: Select all

`bbbb`

rrrr

bbbb

rrrr

Code: Select all

`bbbb`

rbbr

brrb

rrrr

- Wed Jan 11, 2017 2:17 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**319** - Views:
**35371**

### Re: Misunderstanding basic math concepts, help please?

Ho boy! We have Demki insisting that I formally prove that it is impossible to formally prove (or define) anything. And this here shows you didn't read my post. I didn't ask you to prove that you can't prove anything. I asked you to use whatever methodology you propose to replace axiomatic mathemat...

- Mon Jan 09, 2017 9:05 pm UTC
- Forum: Logic Puzzles
- Topic: magic cube
- Replies:
**4** - Views:
**1158**

### Re: magic cube

"It was a joke"

- Sat Jan 07, 2017 6:39 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**319** - Views:
**35371**

### Re: Misunderstanding basic math concepts, help please?

So far you have been rambling on and on about how we can't describe anything, so what makes the 'relationship of patterns of words' that you suggest not be included in the quantifier 'anything'? You have yet to show a single concrete example of how you would do things differently. Could you show wha...

- Mon Jan 02, 2017 5:35 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9676** - Views:
**1426997**

### Re: Coding: Fleeting Thoughts

Because floats cannot represent 1/100 exactly. Ah, ok. Makes sense. So if I did floor(length)==floor(width) then it wouldn't be wrong? (at least it wouldn't slither past the condition) If you did that you would indeed get it to terminate, it probably will not be after the expected number of iterati...

- Sun Jan 01, 2017 11:08 pm UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9676** - Views:
**1426997**

### Re: Coding: Fleeting Thoughts

So yes, you get the expected result for integers. So then, why is float length; float width; length = 10.0; for (width=1.0 ; width=width+.01 ; length==width) print ("still too long"); print ("Finally, perfect!"); wrong? Jose As Korona said, floating point values cannot accuratel...

- Sun Jan 01, 2017 4:37 pm UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9676** - Views:
**1426997**

### Re: Coding: Fleeting Thoughts

Seeing as floating point division is done by dividing the mantissa and subtracting the exponents, in the case of 6.0/3.0, you should get exactly 2.0, as the mantissa are 1.1 and 1.1, and the exponents would be 2 and 1( so we have (1.1 × 2^(2))/(1.1 × 2^(1)) so we get (1.1/1.1) × 2^(1), and since the...

- Fri Dec 30, 2016 2:20 am UTC
- Forum: Language/Linguistics
- Topic: Thinking in words, and noticing errors
- Replies:
**15** - Views:
**2065**

### Re: Thinking in words, and noticing errors

When you have a thought, do you tend to think it in words and sentences? Most of the times, yes, especially when writing text. My thinking has actually shifted from being mostly in Hebrew(first language) to English, probably due to the time I spent on the internet and thus reading a lot of English ...

- Thu Dec 29, 2016 3:54 pm UTC
- Forum: Mathematics
- Topic: Combinatoric commanders
- Replies:
**6** - Views:
**1394**

### Re: Combinatoric commanders

I'll represent the colors by their initials, except I'll use the printers' convention of using K for black, so our colors in color-wheel order are WBKRG. The official convention is to use B for black and U for blue. PM 2Ring refers to the CMYK color model, where K stands for Key and is the black co...

- Thu Dec 22, 2016 2:53 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**58507**

### Re: Infinite Balls and Jugs [solution]

I did not see such a case described, could you describe it for me? Is it that hard to imagine? For each step of the supertask add 10 balls and remove 1. What do you have at midnight? In my point of view, it is underdefined. I am unable to know for any given ball if it is in the jug or not at the en...

- Thu Dec 22, 2016 1:38 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**58507**

### Re: Infinite Balls and Jugs [solution]

You can describe a general case where the balls are un-numbered and everyone (as far as I know) agrees you end up with an infinite number of them. No possibility whatsoever of any other outcome. Yet by assigning each one a number and moving them in a special way, suddenly you (claim that you) actua...

- Tue Dec 20, 2016 5:09 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**58507**

### Re: Infinite Balls and Jugs [solution]

I'll reiterate: an ordinal is not a property of an element in a set. An ordinal is a set that is well ordered, and is defined in a specific way as to represent the class of sets that have an order-preserving bijection to said ordinal. When we say 'the set of balls is isomorphic to omega', we literal...

- Mon Dec 19, 2016 9:44 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**58507**

### Re: Infinite Balls and Jugs [solution]

I believe what he meant was 'we can split this supertask into a well-ordered set of finite tasks isomorphic to omega, each element denoted TAn for some finite ordinal n', at least that's what I got from it.

Edit: some of my own self-nit-picking...

Edit: some of my own self-nit-picking...