## Search found 157 matches

- Fri Dec 16, 2016 1:27 pm UTC
- Forum: Logic Puzzles
- Topic: Word Puzzle.
- Replies:
**6** - Views:
**981**

### 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:
**48966**

### 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:
**319** - Views:
**27712**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**48966**

### 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:
**2231**

### 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:
**48966**

### 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:
**48966**

### 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:
**2231**

### 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:
**2231**

### 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:
**48966**

### 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:
**2321**

### 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:
**1353**

### 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:
**1194**

### 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:
**2859**

### 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...

- Wed Sep 28, 2016 7:11 am UTC
- Forum: Mathematics
- Topic: Vectors and Matrix Determinants
- Replies:
**3** - Views:
**1177**

### Re: Vectors and Matrix Determinants

In addition to cyanoshi's post, I think these 2 videos might help you, at least for the case of 3d vectors:

https://youtu.be/eu6i7WJeinw

https://youtu.be/BaM7OCEm3G0

These 2 videos are part of a series about linear algebra.

https://youtu.be/eu6i7WJeinw

https://youtu.be/BaM7OCEm3G0

These 2 videos are part of a series about linear algebra.

- Mon Sep 26, 2016 7:42 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1738:"Moon Shapes"
- Replies:
**66** - Views:
**5487**

### Re: 1738:"Moon Shapes"

In the same conversation, I also learned how to know whether the moon is waxing or waning: " La lune est menteuse ". The moon is a liar: when she looks like a "D", she's waxing ( c roissante); when she looks like a "C", she's waning ( d écroissante). I always went with...

- Mon Sep 26, 2016 8:05 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1738:"Moon Shapes"
- Replies:
**66** - Views:
**5487**

### 1738:"Moon Shapes"

http://imgs.xkcd.com/comics/moon_shapes.png Title Text: "Whenever I see a picture of the moon where the points go more than halfway around, I assume it's being eclipsed by one of those Independence Day ships and interpret the rest of the image in light of that." What about moons with face...

- Sat Sep 24, 2016 10:00 am UTC
- Forum: Mathematics
- Topic: Dataset of linear systems
- Replies:
**21** - Views:
**2559**

### Re: Dataset of linear systems

kolobisbiko wrote:I want to find the properties of a matrix is there a "tool",software for that?

I don't think matlab can provide such information.....I want 10+ properties

What properties are you talking about?

- Mon Sep 12, 2016 5:13 am UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**7117**

### Re: Goahead52's Math Posts

Goahead, the thing is that all your posts are about number theory, so there's no real "searching for subject"

And we can search post text too.

And we can search post text too.

- Fri Sep 09, 2016 9:14 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1731: "Wrong"
- Replies:
**42** - Views:
**5183**

### Re: 1731: "Wrong"

Also when black hat guy is wrong, it's because he wants to be wrong.

- Fri Sep 09, 2016 6:46 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1731: "Wrong"
- Replies:
**42** - Views:
**5183**

### Re: 1731: "Wrong"

Randall get out of my head. I meet too many people like him

- Wed Sep 07, 2016 3:13 am UTC
- Forum: Mathematics
- Topic: Pay to Win - a game theory problem
- Replies:
**21** - Views:
**2670**

### Re: Pay to Win - a game theory problem

Should they produce a binding contract such that they collect all the money [---] But that only works if they are allowed to do that, which I mistakenly assumed, as it wasn't written in the OP. Right, they can't do that, because neither knows how much "all the money" is. It could have bee...

- Tue Sep 06, 2016 4:03 pm UTC
- Forum: Mathematics
- Topic: Pay to Win - a game theory problem
- Replies:
**21** - Views:
**2670**

### Re: Pay to Win - a game theory problem

He could, but why would he? He doesn't know that A got more, so it's in his interest to defect. Say A got a money and B got b money. Should they produce a binding contract such that they collect all the money into one player's "bank", then they "cash out" a+b money and return ea...

- Tue Sep 06, 2016 12:33 pm UTC
- Forum: Mathematics
- Topic: Pay to Win - a game theory problem
- Replies:
**21** - Views:
**2670**

### Re: Pay to Win - a game theory problem

Well, if they can transfer before, then B could give A all the money he "got", then cooperate while A defects, giving A a+b while b still gets 0(and doesn't lose any because he only transfered the money that was allocated to him)

- Tue Sep 06, 2016 9:16 am UTC
- Forum: Mathematics
- Topic: Pay to Win - a game theory problem
- Replies:
**21** - Views:
**2670**

### Re: Pay to Win - a game theory problem

Ah, I think I have been assuming something not given, that they can transfer the money they were given BEFORE they choose to defect/cooperate. I guess I though too much about Liar Game(a psychological manga that has plenty of interesting games)

- Tue Sep 06, 2016 7:25 am UTC
- Forum: Mathematics
- Topic: Pay to Win - a game theory problem
- Replies:
**21** - Views:
**2670**

### Re: Pay to Win - a game theory problem

I'd say that in that case, the contract will be such that whatever money B gives to A, A returns that amount after A defects and B cooperates, since neither side can know the other's amount. Without a contract, A could always run off with the money. This way each side gains the money that was told t...

- Mon Sep 05, 2016 4:21 am UTC
- Forum: Mathematics
- Topic: Pay to Win - a game theory problem
- Replies:
**21** - Views:
**2670**

### Re: Pay to Win - a game theory problem

If they can talk freely, won't they just produce a contract so that one player, say A, would give all his money to B, then A cooperates and B defects, and they would share the money 50-50?

Sure B could lie about the money, but in the contract A can demand to see the piece of paper of B

Sure B could lie about the money, but in the contract A can demand to see the piece of paper of B

- Fri Sep 02, 2016 9:02 pm UTC
- Forum: Mathematics
- Topic: How to Calculate Pi without a Calculator?
- Replies:
**66** - Views:
**4358**

### Re: How to Calculate Pi without a Calculator?

In the 50?*?<=2000, and such, you can use division and 1 or 2 multiplications. It's just (a+x)*x<=b, with x a digit. I am pretty sure that x=floor(b/a)-1 (with -1 mapped to 0) will always work, but I think that x=floor(b/a) might work sometimes, so unless someone can prove otherwise, that's 2 digit...

- Fri Sep 02, 2016 2:23 pm UTC
- Forum: Mathematics
- Topic: How to Calculate Pi without a Calculator?
- Replies:
**66** - Views:
**4358**

### Re: How to Calculate Pi without a Calculator?

In the 50?*?<=2000, and such, you can use division and 1 or 2 multiplications. It's just (a+x)*x<=b, with x a digit. I am pretty sure that x=floor(b/a)-1 (with -1 mapped to 0) will always work, but I think that x=floor(b/a) might work sometimes, so unless someone can prove otherwise, that's 2 digit...

- Thu Sep 01, 2016 5:03 pm UTC
- Forum: Mathematics
- Topic: How to Calculate Pi without a Calculator?
- Replies:
**66** - Views:
**4358**

### Re: How to Calculate Pi without a Calculator?

In the 50?*?<=2000, and such, you can use division and 1 or 2 multiplications. It's just (a+x)*x<=b, with x a digit. I am pretty sure that x=floor(b/a)-1 (with -1 mapped to 0) will always work, but I think that x=floor(b/a) might work sometimes, so unless someone can prove otherwise, that's 2 digits...