Search found 157 matches

by Demki
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...
by Demki
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...
by Demki
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...
by Demki
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...
by Demki
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...
by Demki
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...
by Demki
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
by Demki
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.
by Demki
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...
by Demki
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 ...
by Demki
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...
by Demki
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...
by Demki
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...
by Demki
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.
by Demki
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
by Demki
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...
by Demki
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...
by Demki
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:
constellation?
Nebula Ring constellation
Stars(and galaxies) form constellations
There's a lightning bolt shaped constellation named after david bowie
Equuleus(little horse) constellation
by Demki
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:
Power? As in power rings(DC comics), power star(mario), lightning bolt powerup in games, horse power
by Demki
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 ...
by Demki
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.
by Demki
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
by Demki
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...
by Demki
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...
by Demki
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.
by Demki
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...
by Demki
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...
by Demki
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?
by Demki
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.
by Demki
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.
by Demki
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
by Demki
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...
by Demki
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...
by Demki
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)
by Demki
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)
by Demki
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...
by Demki
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
by Demki
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...
by Demki
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...
by Demki
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...

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