Do this maths. It R Hard.
-
You guys remind me of the front page trolls who defend people who write their own date libraries. Sure, it's possible to do correctly, but still a WTF.
Math is not programming. You're not concerned with things like "performance" or "memory footprint", and most of the time you're not concerned with readability either.
Is there a simpler proof of FLT than the 100-page elliptic-curve mindfuck by Andrew Wiles? Probably. Would it matter much if someone found it? Not really; it's already been shown to be true, you can already use it as a base for other theorems by reducing them to FLT, all you gain is something more "pure".
It's okay to take a shortcut. But it's okay to take a long route too.
-
Math is not programming. You're not concerned with things like "performance" or "memory footprint", and most of the time you're not concerned with readability either.
You're still concerned with being correct, though, and something that's easier to validate as correct is better. Just like with programming.
And programming is math.
-
∀x y: x → y doesn't always mean ∀x y: y → x
-
Sure. And while you're at it I painted this picture of a woman smiling. It does exactly the same job as the Mona Lisa, so you won't mind that it's hideous and awful because I suck at drawing.
-
Sure. And while you're at it I painted this picture of a woman smiling. It does exactly the same job as the Mona Lisa, so you won't mind that it's hideous and awful because I suck at drawing.
Let's not turn the discussion into a commentary on modern art, shall we?
-
It's nothing to do with modern art. When I draw a misproportioned stick figure it's because I lack the skill to draw anything more aesthetically pleasing, and I freely admit that.
My hypothetical picture is a bad picture. An ugly, aesthetically displeasing mathematical proof is a bad proof (if an elegant one is possible).
We're doing maths for our own amusement here. We're not sitting an exam, let alone trying to work out something that anything real actually depends on. 'If you achieve your aim it doesn't matter how you did it' is irrelevant when there is no aim beyond the doing.
Maths is an art form as well as a science: a beautifully pure art from because it encompasses pure ideas and doesn't have to overcome the artist's and the medium's physical limitations, in the same way that it's a beautifully pure science because it doesn't have to contend with experimental error. Aesthetics is absolutely relevant. A really good proof is a thing of beauty, something a mathematician strives to do as well as possible for its own sake.
-
We're not sitting an exam, let alone trying to work out something that anything real actually depends on.
Yet that didn't stop you and @dkf spending a week tearing holes in what started as a simple piece of logical deduction that answered the question
-
Yet that didn't stop you and @dkf spending a week tearing holes in what started as a simple piece of logical deduction that almost answered the question
FTFY
-
My hypothetical picture is a bad picture.
Maybe. But make it into a political cartoon, and it matters a lot less. And Randall Munroe gets quite decent viewership despite mostly drawing ugly stick figures. Because there's more than aesthetics to that.
I'm not even sure what you're arguing. That a proof you deem "ugly" is just as bad as an invalid one? It's not. An ugly proof is still usable, and still valid.
-
It was disgusting. It didn't start as something that answered the question, but even after it was manhandled by main force into something that did, it was hideous. It certainly was not simple. It was offensive to me that someone should present that with the claim that it was 'as good'. If we were actually trying to work this out to use the answer, I wouldn't have minded (much).
I'm not even sure what you're arguing. That a proof you deem "ugly" is just as bad as an invalid one?
No, that it's not as good as a good one.Maybe. But make it into a political cartoon, and it matters a lot less. And Randall Munroe gets quite decent viewership despite mostly drawing ugly stick figures. Because there's more than aesthetics to that.
Do I have to spell every damn thing out? Use the context. And now who's discussing modern art?An ugly proof is still usable
But we're not using it. We're looking at it purely for entertainment. Maths has many functional uses, of course, and in the case of proving something in order to use it what matters is that you get there correctly. But there's more to maths than that. Did you just ignore every single thing I said?
-
Are we getting close to CLOSED INVALID yet?
-
Shush, we're trying to have a flamewar here.
-
Are we getting close to CLOSED INVALID yet?
No, the proof eventually made it to the FIXED state. It just bounced back to the developer a few times. Some of us would like to refactor.
-
Uh-huh. Check your flags.
-
Check your Ms.
-
-
In a maths exam, it is better to arrive at the wrong answer for the right reason, than to arrive at the right answer for the wrong reason.
-
Multiple guess or open answers?
-
Maths is an art form as well as a science: a beautifully pure art from because it encompasses pure ideas and doesn't have to overcome the artist's and the medium's physical limitations, in the same way that it's a beautifully pure science because it doesn't have to contend with experimental error. Aesthetics is absolutely relevant. A really good proof is a thing of beauty, something a mathematician strives to do as well as possible for its own sake.
I think there's two question getting mixed up here.
One, was @RaceProUK's proof correct?
She missed making some clarifications that were implicit in her approach but were correct when spelled out, so after some amendments, the proof was objectively correct.
This is what @RaceProUK cares about, from what I've read.
Two, was @RaceProUK's proof good?
This is a value judgement, and it refers to how "elegant" the resulting proof is, how concise, how error prone the approach is, etc. I'm of the opinion that it isn't particularly good. It's not the approach I would take, nor one I would recommend in general.
This is what most people here seem to be arguing. It would probably be more successful if you stopped trying to prove her wrong, which you can't because her proof is objectively correct, and conceded that she is correct but you don't like it. Which is true, but @RaceProUK might not care about it and so the argument might stop.
-
It would probably be more successful if you stopped trying to prove her wrong, which you can't because her proof is objectively correct, and conceded that she is correct but you don't like it.
... Have you been reading this thread at all?
-
(n+9)(n-10)=0
n = -9 and n=10?
Since we can't have a negative number of sweets in a bag, n=10
-
IOU 9 SWEETS
-
That's a piece of paper not a sweet
-
It's 9 fewer (i.e., -9) sweets compared to what you should have! I have a sweet deficit! <so get off my lawn!>
-
Disagree
-
...And X gets the square!
-
I don't think I've had any multiple guess maths exams.
-
... Have you been reading this thread at all?
Yes, and I noticed that the thread was quiet for two weeks before @OffByOne tried to prove her wrong, and managed instead to show some fundamental misunderstandings about the exercise. Which, ironically, were masked by blindly following the elegant method without reasoning about what he was doing.
-
I've had some. They aren't necessarily easy when the teacher includes answers that cover common mistakes.
Also, standardized tests.
-
You can have a negative number of sweets.
For example, if you are physically holding 0 sweets but owe me 9.
-
…I don't even know where to begin telling you how retarded that argument is…
-
Sure, because it's right.
You would have to take possession of 9 sweets, and give them to me, before you could have any of your own.
-
That's what they used to say about having zero sweets, too.
-
Why the fuck am I still having to defend all the shit I worked out a fucking month ago?
Fuck this shit.
-
the thread was quiet for two weeks before @OffByOne tried to prove her wrong,
I'm slowly catching up on new and unread threads. "New" in this context is a rather stretchy designation, because work
catching up on WTDWTF.and managed instead to show some fundamental misunderstandings about the exercise. Which, ironically, were masked by blindly following the elegant method without reasoning about what he was doing.
'scuse me? What fundamental misunderstandings about the exercise did I show? How exactly didn't I reason about what I was doing?
-
Why the fuck am I still having to defend all the shit I worked out a fucking month ago?
You don't have to. You chose to come in here and do it.
Just FYI.
-
You don't have to. You chose to come in here and do it.
Just FYI.
of course the same is true for those that are attacking her defense. they could move on if they wanted to.
-
Well, yes. True.
Obviously the best solution is to enter the thread and type something like "Turd." And then hit mute and never come back.
-
-
-
You chose to come in here and do it.
And you chose to call me an idiot in another thread without even considering the possibility I was making a joke.So don't be surprised if I think you're being about as sincere as a politician.
-
I call everybody an idiot all the time forever. That doesn't mean anything. Idiot.
-
Yeah, don't be surprised if I don't believe a damn thing you say either
-
Yes, and I noticed that the thread was quiet for two weeks before @OffByOne tried to prove her wrong, and managed instead to show some fundamental misunderstandings about the exercise. Which, ironically, were masked by blindly following the elegant method without reasoning about what he was doing.
So, why did you address your remark to probably the one member of the prosecution who's been at most pains to admit that it is technically right?
-
So, why did you address your remark to probably the one member of the prosecution who's been at most pains to admit that it is technically right?
That is a very good question. Given that we are on WTDWTF, it will likely not get an answer.
-
Well, yes. True.
Obviously the best solution is to enter the thread and type something like "
TurdSurd." And then hit mute and never come back.MTFY
-
So, why did you address your remark to probably the one member of the prosecution who's been at most pains to admit that it is technically right?
The bit I quoted was the most clear example of the difference between correct and good I could find on a quick search. I did not mean to imply that you specifically were trying to prove her wrong. I intended the "you" in the last paragraph in the general, plural form. To apply only to the people doing it. Sorry, my bad. Should have been more clear on that.
Speaking of which:
'scuse me? What fundamental misunderstandings about the exercise did I show? How exactly didn't I reason about what I was doing?
When you (this time I do mean the specific you) saidAssume the question, instead of having n² - n - 90 = 0, had n² - 2n - 80 = 0 instead.
And laterYou'd say, "That equation has -8 and 10 as solutions, -8 is nonsensical in the context, so 10 is the correct answer and that checks out with what is given about the candies".
Would you have noticed with your method that the proposed equation is actually wrong?
No, because n² - 2n - 80 = 0 has different solutions than n² - n - 90 = 0.
[...]
Handwave all you want, but that doesn't make any equation that happens to have n = 10 as a possible solution correct. Only the equation in the original question is correct.Literally the first sentence in the exercise is "There are n sweets in a bag." Any later reference to n must, therefore, unequivocally refer to the number of sweets in the bag. Since a bag cannot contain a negative number of sweets, this removes every negative number from consideration.
The exercise then gives a probability for a specific scenario. This further limits n to a finite set of values. Specifically, only one: 10.
As a consequence, any equation where n = 10 holds, is true. Because n is the number of sweets in the bag, and that number can't be anything other than 10. If it was, the probability cited would not be 1/3.
Far from proving her wrong, what you did is show the kind of equations where her approach is actually more valid. If the exercise asked you "show that n^3 - 1000 = 0", the constructive approach would fail you because you would essentially have to work n out, and test it.
In practice, the approach the exercise guided you towards only works for equations that are trivially constructible from the probability equations, without working n out. Her approach works for every other equation where n = 10, and that you can only prove by working out that n = 10.
Which you would do by reaching n^2 - n - 90 = 0, solving the quadratic equation, and discarding -9.
-
In practice, the approach the exercise guided you towards only works for equations that are trivially constructible from the probability equations, without working n out.
In practice, that was the problem presented.
-
In practice, that was the problem presented.
Yes, but then OffByOne offered a problem where that approach doesn't work. Which is why I said he didn't understand the exercise and was simply following a process blindly. Once he reached the limit of that approach, he thought everything outside of it must be wrong. Because he offered as "wrong" examples that weren't, and that would make RaceProUK's approach right.
-
Yes, but then OffByOne offered a problem where that approach doesn't work. Which is why I said he didn't understand the exercise and was simply following a process blindly.
I think you misunderstood @OffByOne's point, then, because the technique relied on the equation being correct and knowing the equation.
Because he offered as "wrong" examples that weren't, and that would make RaceProUK's approach right.
Yeah, that's the opposite of what I got out of that post.
