Search found 599 matches

by Cauchy
Thu Jul 06, 2017 6:35 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

thoughts for instance don't exert gravitational pull. With this line, I demonstrate that my distinction exists. There''s no logical fallacy here. Similarly, what's the mass of three? What's the angular momentum of this sentence? In order for A and B to interact they must be a part of the same whole...
by Cauchy
Tue Jul 04, 2017 2:54 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

What does this have to do with your misunderstanding basic math concepts? The difference between a tree and a thought is that one is an object and one is a pattern. The physical object that the thought is a pattern of is the brain. I don't understand your argument because I skip most of your posts w...
by Cauchy
Sun Jun 04, 2017 12:02 am UTC
Forum: Mathematics
Topic: [Linear Algebra] Finding an orthogonal vector
Replies: 3
Views: 1054

Re: [Linear Algebra] Finding an orthogonal vector

Don't you do that determinant thing that gets you the cross product? For n-1 vectors in R^n, look at the matrix [v_11 v_12 ... v_1n] [v_21 v_22 ... v_2n] . . . [v_{n-1}1 v_{n-1}2 ... v_{n-1}n] [x_1 x_2 ... x_n] where the x_i is 1 in the ith position and 0 everywhere else, and take its determinant. I...
by Cauchy
Sat May 06, 2017 7:21 am UTC
Forum: Mathematics
Topic: Halting Problem
Replies: 200
Views: 11384

Re: Halting Problem

Big post, but I wanted to take a crack at explaining this and clearing up some of your problems. Let me know if and when something confuses you. One thing to note is that programs by their very nature are required to give the same output when fed the same input, every time, without fail. Oracle isn'...
by Cauchy
Tue Mar 28, 2017 5:00 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 4082

Re: Two secrets

For N = 3, any two-element subset will work. 0 questions. For N = 4, ask about any two-element subset. If the answer is "yes", you have it; if the answer is "no", then its complement works. 1 question. For N = 5, asking about 0, 1, 4, or 5-element subsets is fruitless (since the ...
by Cauchy
Tue Jan 31, 2017 7:03 am UTC
Forum: Mathematics
Topic: variance of a sum of iid random variables
Replies: 2
Views: 1321

Re: variance of a sum of iid random variables

>-) wrote:sum i,j from 1,1 to n,n of E[y_i y_j]
= sum i,j from 1,1 to n,n of E[y_i] E[y_j] (by independence of y_i)


This is not true, because, for example, y_1 and y_1 are not independent. You end up with n(n-1) terms of the form E[y_i] E[y_j] for i != j, and n terms of the form E[y_i^2].
by Cauchy
Thu Dec 08, 2016 9:48 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

Who the fuck cares whether mathematics can define something in an absolute sense? It's only you. You're the one putting words in other people's mouths, both in your posts explicitly and in axiomatic mathematics' mouth claiming that it wants to try to deal with absolutes. Everyone (except you) knows ...
by Cauchy
Mon Dec 05, 2016 6:07 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

You're the one claiming that everything ever is relative, Treatid. Are you saying you have an actual counterexample to the first law of thought, or is this more of your waving wildly in the air? You seem to want to say 1. Axiomatic mathematics is an absolute system. 2. There are no absolute systems....
by Cauchy
Sun Dec 04, 2016 8:43 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

It was argued that since balls have special memories of their past digits and Hilbert's Hotel has an incompetent assistant manager, the limits should actually be different. You sound unconvinced. 1. In the original, remove-the-lowest-ball game, there exists at some point a ball with the label "...
by Cauchy
Sat Dec 03, 2016 4:28 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

There was a comment a few pages back that I didn't pick up properly at the time, where it was said "but if the sequences are the same at every point, then how can the limit be different"? And here's the answer to that... f i and g i are different functions... the sequences of functions is...
by Cauchy
Sat Dec 03, 2016 4:08 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

What is a reference frame in mathematics? You need to be more specific. You say "the reference frame at integer zero" and "the reference frame at infinity", but what do those mean? Showing one example of an equivalent equation in those two frames does very little to enlighten. Do...
by Cauchy
Tue Nov 29, 2016 7:30 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

Okay, axiomatically defined things are defined relative to the language they're written in, or something. So what? You're the only one who seems to think that the absolute vs. relative divide matters, or that axiomatic mathematics not being "absolute" damns it. The goal of axiomatic mathem...
by Cauchy
Wed Nov 23, 2016 1:46 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

I can't see the balls as anything but interchangeable. That is, if I take the balls with labels 2 and 3, and swap their labels, I haven't changed anything in the jug. I disagree. If you look at a single ball in the first game, you see it enter at a step, and leave at a step, and those steps are def...
by Cauchy
Tue Nov 22, 2016 6:22 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

So, I think that we can resolve the paradox in this way: We have a sequence of sets of balls that is different from the sequence of sets of balls in the first game; and a sequence of sets of labels which is the same as the sequence of sets of labels in the original game. At midnight, we have an inf...
by Cauchy
Sun Nov 20, 2016 6:33 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

Suppose we have a sequence of sets, where S n is defined as {f 1 (n), f 2 (n)}, where f 1 (n) = (-1)^n, f 2 (n) = (-1)^(n+1). Is the limit of this sequence {1, -1}? Or is the limit of the sequence {lim f 1 , lim f 2 }? It's {-1, 1}. Maybe a more enlightening example would be that if R_n = {1/n}, th...
by Cauchy
Sat Nov 19, 2016 7:21 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

Why should a limit of a sequence care about the specific formula you happen to use to define the terms of the sequence? It's certainly not true for sequences of real numbers, so why should it suddenly become true for sequences of sets? This is what I can't understand about your wanting Scenarios A a...
by Cauchy
Fri Nov 18, 2016 11:42 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

Your error occurs at the bolded statement. There is no reason to believe that a property that exists at every finite step also exists after an infinite number of steps. And yet you believe that so vehemently in Scenario A, that no ball with an "infinite label" is added because there's no ...
by Cauchy
Fri Nov 18, 2016 5:21 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

How can Scenario A and Scenario R have different ends to their supertasks? They're the same after each step, so they must have the same limit, if such a limit exists. Specifically, claims keep being made about how in Scenario A, the jug must be empty, because no non-naturally-numbered ball is ever a...
by Cauchy
Thu Nov 17, 2016 7:48 pm UTC
Forum: Logic Puzzles
Topic: Lost Car Keys
Replies: 1
Views: 1891

Re: Lost Car Keys

Before checking your pocket, there's a 1/5 chance the keys fell out during the first meeting, a 4/5*1/5 = 4/25 chance the keys fell out during the second meeting, a 4/5*4/5*1/5 = 16/125 chance the keys fell out during the third meeting, and a 4/5*4/5*4/5 = 64/125 chance the keys are still in your po...
by Cauchy
Fri Nov 04, 2016 9:14 pm UTC
Forum: Forum Games
Topic: Three words, one solution
Replies: 53
Views: 4589

Re: Three words, one solution

If it had just been "Ring" I would have said Mega Man bosses.
by Cauchy
Fri Oct 28, 2016 7:10 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71051

Re: Infinite Balls and Jugs [solution]

I'm not sure why we should just blindly accept that the pointwise limit of the sets is the correct one. I agree that no other limit makes sense, but in a lot of contexts we simply say "there is no limit" when the pointwise limit fails to do what we want. And if it can't even preserve cardi...
by Cauchy
Fri Oct 28, 2016 7:06 pm UTC
Forum: Forum Games
Topic: Three words, one solution
Replies: 53
Views: 4589

Re: Three words, one solution

Mile
by Cauchy
Mon Oct 17, 2016 5:59 pm UTC
Forum: Mathematics
Topic: Proving angles are equal in a triangle in a circle.
Replies: 15
Views: 2467

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

I don't really understand why people are saying to add the center, or construct right angles, or what have you.

In terms of circle arc measures, what is the measure of angle TAC? What is the measure of angle ABC? You should have theorems about both of these.
by Cauchy
Sat Oct 08, 2016 8:36 pm UTC
Forum: Mathematics
Topic: uniform acceleration
Replies: 3
Views: 1750

Re: uniform acceleration

If the train accelerates uniformly from a speed of 0 to a speed of v, what is its average speed over this interval? If the train decelerates uniformly from a speed of v to a speed of 0, what is its average speed over this interval?
by Cauchy
Tue Sep 27, 2016 3:09 am UTC
Forum: Mathematics
Topic: Pay to Win - a game theory problem
Replies: 21
Views: 4170

Re: Pay to Win - a game theory problem

Once you open up lying, then why should I believe your inflated number? If I know you're liable to inflate your number, then I have no reason to assume that the number you report is correct.
by Cauchy
Wed Sep 14, 2016 8:42 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

My eyes are rolling back in my head. Your last post is so rambling that I can barely comprehend it. I'll try to, though. I'm pretty sure there is an intended difference between mathematics and physics. A physical model/description/map has value according to how well it describes an actual physical p...
by Cauchy
Sat Sep 03, 2016 5:13 pm UTC
Forum: Mathematics
Topic: statistics
Replies: 2
Views: 1437

Re: statistics

Why is that the correct value for part (a)?

What does margin of error mean? What does the poll say the actual percentage is? What is the 5% level of significance?
by Cauchy
Sat Sep 03, 2016 7:14 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

Absolutist assumption A given !x is changed. x is not directly changed. Obviously if !x is changed then C is also changed. However, x is an absolute value and does not depend on C or !x. x (before) = x (after) What do you mean, !x is changed? How? Why? The complement of something (b...
by Cauchy
Wed Aug 31, 2016 8:52 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

Cauchy asks for a couple of conditions: 1. No leaping tall gulfs of understanding/description by using impossible presumptions. 2. The result should say something that can be applied: There should be mathematics involved, not 'just philosophy'. That's not how I'd phrase what I said at all. I want y...
by Cauchy
Tue Aug 30, 2016 7:54 am UTC
Forum: Mathematics
Topic: Goahead52's Math Posts
Replies: 148
Views: 11649

Re: Goahead52's Math Posts

If you have to consult a lookup table, why not just store the number of primes itself? That way, you don't have to do any summation after you look up numbers.
by Cauchy
Sat Aug 27, 2016 5:27 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

Cauchy: I hope you are also a teacher outside these forums. Even when you think people are wrong - you don't tell them they are wrong, you give them a carefully measured piece of rope exquisitely judged to let them hang themselves (realise where they have made a mistake). Your consistent constructi...
by Cauchy
Fri Aug 26, 2016 10:06 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

I think that they, and axiomatic mathematics, are missing how important the difference between "absolutely distinct in every conceivable way" and "mostly separate, but not quite entirely so" is. What does it mean for two systems to be "mostly separate, but not quite entirel...
by Cauchy
Thu Aug 25, 2016 10:20 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

If I'm running two different VMs on my computer at the same time, and one crashes, it doesn't mean that the other has to go down with it. In fact, the VMs probably don't interact with each other at all. This is the way that different axiomatic systems are separate. If two different computers run the...
by Cauchy
Tue Aug 23, 2016 4:31 pm UTC
Forum: Mathematics
Topic: Goahead52's Math Posts
Replies: 148
Views: 11649

Re: Goahead52's Math Posts

So if x=(a+b)^2 and x-a^2+2ab+b^2 is then going to tell you something? x = (a+b)^2 is not an identity: if x = 2, a = 1 and b = 3, it's clearly false. So if you assert that it's true, you find out something about x, a and b. That's why x-(a^2+2ab+b^2) can be evaluated to 0, under the premise that th...
by Cauchy
Mon Aug 22, 2016 2:34 pm UTC
Forum: Mathematics
Topic: Goahead52's Math Posts
Replies: 148
Views: 11649

Re: Factorization of odd semi prime is over!

Goahead52 wrote:A(A-y+1) mod (p*q-2)=A-(2*y)+4



Since pq=A, we get that A(A-y+1) = A - 2y + 4 (mod (A-2)).

Since A is congruent to 2 mod A-2, we find that 2(2-y+1) = 2-2y+4 (mod (A-2)).

But this is an identity. That is to say, it's true for any values of A and y. So its truth doesn't tell us anything about y.
by Cauchy
Mon Aug 22, 2016 2:22 pm UTC
Forum: Logic Puzzles
Topic: Factorial puzzle
Replies: 6
Views: 2807

Re: Factorial puzzle

The link between m and n is that their product seems to be constant for a given k. I would be fairly surprised if there were solutions not generated by the algorithm I described.
by Cauchy
Mon Aug 22, 2016 1:41 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

I googled "does salt taste like sodium and chlorine together" and literally the first result is a Stack Exchange question whose answer effectively says that yes, salt tastes like sodium cations and chlorine anions together because the salty taste is triggered by the sodium cations once the...
by Cauchy
Fri Aug 19, 2016 2:00 am UTC
Forum: Logic Puzzles
Topic: Factorial puzzle
Replies: 6
Views: 2807

Re: Factorial puzzle

What is the point of having m and n? The Euler totient function is multiplicative , so unless you plan to have solutions with m and n sharing a factor, we can just talk about mn*phi(mn). Really, though, we should be splitting m and n up across their prime factors. So we have m = p_1^{m_1}p_2^{m_2}.....
by Cauchy
Sun Aug 14, 2016 8:22 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 48270

Re: Misunderstanding basic math concepts, help please?

What is the complement of an axiomatic system? Does it have the same symbols? The same well-formed formulae? The same rules of inference? The same axioms? You use the term like you expect us to know what it means, but no one else talks about the complement of a theory. Te complement of a set, I know...
by Cauchy
Fri Aug 12, 2016 2:27 pm UTC
Forum: Logic Puzzles
Topic: Sharing secret information publicly
Replies: 27
Views: 4691

Re: Sharing secret information publicly

Once I found the best and elegant solution I will post it. Just letting you know, it's already in the thread. Tirear posted most of it, and I put the finishing touches on it. The Fano plane solution (which you have yet to accurately write down) is pretty, and a natural jump when you're talking abou...

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