## Search found 213 matches

- Fri Apr 14, 2017 12:04 am UTC
- Forum: Religious Wars
- Topic: What is log² x?
- Replies:
**11** - Views:
**9696**

### 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:
**32** - Views:
**24286**

### 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:
**4403**

### 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:
**6194**

### 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:
**338** - Views:
**78807**

### 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:
**4063**

### 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:
**338** - Views:
**78807**

### 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:
**9990** - Views:
**2000562**

### 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:
**9990** - Views:
**2000562**

### 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:
**9990** - Views:
**2000562**

### 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:
**11548**

### 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:
**2911**

### 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:
**120190**

### 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:
**120190**

### 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:
**120190**

### 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:
**120190**

### 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...

- Fri Dec 16, 2016 1:27 pm UTC
- Forum: Logic Puzzles
- Topic: Word Puzzle.
- Replies:
**6** - Views:
**5256**

### Re: Word Puzzle.

In that case you need to explicitly define the dictionary you use. If you, for instance include Hebrew words, it is quite likely you'll be able to solve it since every letter can be a consonant. It also opens up to something like chinese where each letter is a word in and of itself, and iirc order d...

- Sat Dec 10, 2016 1:05 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

Since at the limit, (1/2) n and (9/10) n are both equal to 1... You mean 0 @kryptonaut: "1,2... and so on" is used to refer to the set of natural numbers greater than 0. If people want to specify some set that contains infinitely big numbers(such as the superreals), they say so explicitly...

- Mon Dec 05, 2016 8:28 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**78807**

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

The axiom (for all x, x=x), says nothing about x, that is why we have the universal quantifier 'for all'. That axiom is about a relation we choose to call equality(or label with =), and all it says is that equality(=) is reflexive. If you say 'but equality(=) isn't reflexive!', then you aren't using...

- Tue Nov 29, 2016 4:20 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

When we say '0×∞ can be anything', we don't mean the number zero times some notion of ∞, because that is undefined under most notions of infinity(and where it is defined we lose some properties, like multiplicative inverses). What we mean is that if we have 2 real-valued functions f(x) and g(x), suc...

- Tue Nov 29, 2016 3:14 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

The only way for that tower to have nonzero size is if each piece decreases in size(say the size of the section halves with each step), so wherever you point, it is part of some finite section corresponding to a natural number, if you point from above straight down at the top, there is no number you...

- Sat Nov 26, 2016 9:43 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

3 things I'd like to address about kryptonaut's posts(should you wish, you may ignore this post, and I don't really plan on writing here in the near future): 1. The natural numbers are already ordered as the ordinal omega, so when we say 'at step n, where n is a natural number, do this_n', we mean t...

- Thu Nov 24, 2016 3:02 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

@xias, omega+1 has the same cardinality as N, that is it is countably infinite, but yes, there is no order preserving bijection between omega+1 and omega.

But yes, HH is usually defined to be isomorphic to omega

But yes, HH is usually defined to be isomorphic to omega

- Tue Nov 22, 2016 5:36 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

The ordinal omega is not a natural number, where did a ball with label omega come from in the S T D game? Did it pop out of thin air into the jug?

You can't say it was in S because you agreed S had only natural numbered balls.

You can't say it was in S because you agreed S had only natural numbered balls.

- Mon Nov 21, 2016 11:31 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

The answers to both of these at, for example, step 2, is: a) the set of natural numbers from 3 to 20; and b) the union of the set of natural numbers from 1 to 9 with the set of natural numbers from 11 to 20 . I believe you mean from 11 to 19 I'd like to add that the 'game' I proposed earlier better...

- Thu Nov 17, 2016 5:35 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

There's the thing, in scenario 1 you can't have a ball with a label, because we only ever add balls with labels that have natural numbers on them, there is no magic smoke that produces that 'infinitely big' label in scenario 1 In scenario 2, however, we basically map the natural numbers to a string ...

- Thu Nov 17, 2016 3:52 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

Yes there was that typo. Your 'problem' with my scenario 1 is that you failed to read "at every step n, where n is a natural number", that is, we only take steps for natural numbered steps, and yes, there are countably infinite such steps. Where does you supposed "countably infinite l...

- Thu Nov 17, 2016 2:20 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

Where did the infiniteth step comes from? The problem does not mention any step that does not correspond to a natural number. Consider this 2 scenarios: 1: the jug starts(step 0) with an object that is labeled 0, at each step n, where n is a natural number, remove the object labeled with a string of...

- Sat Nov 12, 2016 9:00 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

Your example strikes me as very similar to the proof that pi = 4 I think the problem with this 'proof' is that the tangent to the angular shape never approaches that of the circle, so the final shape after infinite reversing of corners is not a circle even though it may look like one The limit of t...

- Fri Nov 11, 2016 7:28 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

Since you only add balls labeled with a finite string of digits, there is no point at which a ball with an infinite string of digits is added, so 0.999... is never added to the jar, and thus is not in the jar.

- Fri Nov 11, 2016 10:10 am UTC
- Forum: Forum Games
- Topic: Three words, one solution
- Replies:
**53** - Views:
**9384**

### Re: Three words, one solution

gewoonm wrote:Very interesting! But not the answer!

AFAIK its not clear where Commodore got its name from, you think it's from a person?

'Commodore' is a rank in a navy

- Thu Nov 10, 2016 2:35 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

There are an infinite number of naturals, but each one individually is a finite number. And at midnight after an infinite number of steps all the natural-numbered balls have been removed, leaving 'only' the infinitely many infinite-numbered balls behind. How about looking at the problem as: Evaluat...

- Thu Nov 10, 2016 12:35 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

There are an infinite number of naturals, but each one individually is a finite number. And at midnight after an infinite number of steps all the natural-numbered balls have been removed, leaving 'only' the infinitely many infinite-numbered balls behind. How about looking at the problem as: Evaluat...

- Wed Nov 09, 2016 8:46 pm UTC
- Forum: Forum Games
- Topic: Three words, one solution
- Replies:
**53** - Views:
**9384**

### Re: Three words, one solution

**Spoiler:**

- Wed Nov 09, 2016 9:28 am UTC
- Forum: Forum Games
- Topic: Three words, one solution
- Replies:
**53** - Views:
**9384**

### Re: Three words, one solution

**Spoiler:**

- Tue Nov 01, 2016 5:11 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**120190**

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

The problem with limits to infinity is that they often don't conserve some of the structure, for example is the famous 'proof' that pi=4, by taking a square and in each step cutting rectangular chunks out of it so that the pointwise limit is a circle, yet in every step along the way we have a shape ...

- Thu Oct 20, 2016 6:41 pm UTC
- Forum: Mathematics
- Topic: Finding a Quadrilateral for N Points
- Replies:
**20** - Views:
**5622**

### Re: Finding a Quadrilateral for N Points

Hint for an upper bound: each line segment of the quadrilateral contains at most 2 of the points.

- Mon Oct 17, 2016 9:42 pm UTC
- Forum: Mathematics
- Topic: Proving angles are equal in a triangle in a circle.
- Replies:
**15** - Views:
**4405**

### Re: Proving angles are equal in a triangle in a circle.

doogly wrote:You can't just "have theorems." That's a kind of cheating. You have to draw things.

You also have to locate the center with just an unmarked straight edge

- Thu Oct 13, 2016 4:03 pm UTC
- Forum: Logic Puzzles
- Topic: Solitaire game
- Replies:
**4** - Views:
**3750**

### Re: Solitaire game

In the worst case you'd keep getting only balls with v=1, or v=0. thus never emptying the urb. A greedy strategy would be to remove the balls with v=1, or v=0, until you have only balls with v=-1 I supposed if you can calculate v fast enough, you could make a strategy relating to whether the next ba...

- Sun Oct 02, 2016 8:28 am UTC
- Forum: Mathematics
- Topic: 'Math is Pseudoscience and Fake Astrology' (Strange, Fringe Views by Prominent Figures)
- Replies:
**10** - Views:
**6492**

### Re: 'Math is Pseudoscience and Fake Astrology' (Strange, Fringe Views by Prominent Figures)

Well, in essence, mathematics is "fiction", as in, we choose what our alphabet is, what laws of deduction we wish to follow, what assumptions we make(axioms), and then we see what we get out of it. The act of applying the results to real world data is up to the physicists/chemists/biologis...