So we all know that to find the length of a hypotenuse you use the formula A squared + B squared = C squared. What happens, however, if A and B = 1 ? Did Pythagoras note this problem? Is 2 the only number with an infinite decimal for a square root? How do you find the length of the hypotenuse in this situation?
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Anonymous2007-06-03 14:25 ID:t7dKdTW3
Obviously talking about right triangles here...
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Anonymous2007-06-03 14:32 ID:ArXsoL8C
>>1
You just say the answer is root 2 and tell the decimal fraction equivalent to get the hell out.
Most roots of naturals are irrational. Root 3, 5, 6, 7, etc.
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Anonymous2007-06-03 14:49 ID:aR38uIKO
>>3
More specifically, if N is a positive integer and sqrt(N) is not an integer, than sqrt(N) is irrational.
>>8
He said: "Most roots of naturals are irrational. Root 3, 5, 6, 7, etc."
I said: "Any integer which has a non-integral square root has an irrational square root."
Note how his statement gives: existence of integers with irrational square roots, and 4 examples. Mine gives: existence of integers with irrational square roots, and a complete classification of said integers. Hence, it is more specific.
If you disagree, you have no idea of what specificity and generality mean in the context of mathematics.
>>11
He answered the question at hand (are there natural numbers other than 2 which have irrational square roots), and I SPECIFIED those numbers exactly. Notice how SPECIFY and SPECIFIC are similar? Fucking 7th graders need to get out of my /sci/.
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Anonymous2007-06-03 21:21 ID:QwKrPK3o
A GENERAL rule that SPECIFIES which numbers belong to the set, now STFU.
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Anonymous2007-06-03 21:24 ID:QwKrPK3o
A GENERAL rule that SPECIFIES which numbers belong to the set, now STFU.
>>14
I made a more specific version of his statement; he said that natural numbers with irrational square roots exist, I said that they exist and that the set of such numbers is equivalent to the set of non-square natural numbers. If you don't see how this adds specificity to his statement, I don't know what else to say - you're either retarded, or you genuinely have no idea what "specific" and "general" mean.
Also, since you won't just shut up and gb2/middleschoolalgebra/, I'm going to point out that Generalization is a well defined part of math and logic. http://en.wikipedia.org/wiki/Generalization_(logic)
Dude, i totally see how you specified the rest of the set, however, i'm no mathematician, but you'll often see it said:
"x y and z belong to the set Q. In fact, the general rule is that x belongs to Q if Z."
I'm pretty sure that can be said to be generalizing. I think that the main confusion here is that maybe you're using the strictly mathematical/logical definition of 'generalization', but it also has a meaning in spoken english:
gen·er·al·ize:
1. to infer (a general principle, trend, etc.) from particular facts, statistics, or the like.
2. to infer or form (a general principle, opinion, conclusion, etc.) from only a few facts, examples, or the like.
Now i'm pretty sure the above is what happened in this thread. However, somehow i also think you are right because the definition of specify:
1. to mention or name specifically or definitely; state in detail
There's no need to sling around insults, I mean we're both on fucking 4chan arguing about the most trivial and ridiculous things.
"gen·er·al·ize:
1. to infer (a general principle, trend, etc.) from particular facts, statistics, or the like.
2. to infer or form (a general principle, opinion, conclusion, etc.) from only a few facts, examples, or the like."
"There exist elements with property P, and they are precisely the elements with property Q"
This is NOT A FUCKING GENERALIZATION. Not mathematically, not colloquially. I'm not saying it is any less general: it simply restates the first with more specificity. You don't generalize something by turning an existence statement into a classification statement. A generalization would be something like:
"There exist elements satisfying property R(n) for any relevant n, and for some value of n, R(n) is equivalent to P"
In this case, for instance, a generalization would be "There exist natural numbers with irrational n-th roots for any natural number n > 1." Then, in the case n = 2, we see that there exist natural numbers with irrational square roots.
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Anonymous2007-06-05 3:51 ID:ezLnTka/
"general case" surely you have heard of such a thing - you specified the general case, LOLz
<Wikipedia>
For any two related concepts, A and B; A is considered a generalization of concept B if and only if:
* every instance of concept B is also an instance of concept A; and
* there are instances of concept A which are not instances of concept B.
</Wikipedia>
Let A be the statement "If N is a positive integer and sqrt(N) is not an integer, then N is irrational" and B be the statement "If N is a positive integer having value 3, 5, 6, or 7, then sqrt(N) is odd".
Then every statement of B is also an instance of concept A (since 3,5,6, and 7 are positive integers) , and there exist instances of concept A (i.e., positive integers whose square roots are not integers) that are not instances of concept B. Then statement A is a generalization of concept B.
If anyone sees any serious flaws with the above reasoning, please point them out.
What >>3 etc. did was "specify" (i.e. define) the general rule for determining whether the square root of a number is irrational. Then the rest of the thread used the logical meaning of "specify" (one case of a general statement) whereas >>3 etc. use the meaning "to define".
>>24
Yes, four examples was given, and then a rule. Clearly, the rule wasn't derived from the examples, so no generalization.
However, no one mentioned generalization. The phrases used were 'more specifically' (>>4) vs. 'more in general'(>>6).
I stand by my claim (me being >>6 and >>11) that a general rule is more general that 4 specific examples. That is my claim, and the whole of my claim.
>>27
This thread was over at >>5.
This is an entirely recreational (read: pointless) semantics nitpick, and would have been gone now if you people would stop bumping it.
>>28
/sci/ threads last for ages. They don't randomly disappear after a few days like /b/ threads. If you look in the archive, some of those threads are > a yr old.
>>30
"(FYI, toothpaste means moron, and I'm just going to continue saying such in the face of all evidence to the contrary.)"
Doesn't that make you the moron (ie continuing to say something in the face of all evidence to the contrary)?
>>31 >>30 here. I was parodying his "That's my claim and I stand by it" despite the fact that it is totally irrational given the definitions of generality.
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Anonymous2007-06-06 18:09 ID:Cqi26e3c
hypotenuse for a rightangled triangle is root 2, basic trig
>>32
I actually begged the question in >>28 by using the expressions "general rule" and "specific examples". Since that is valid english usage, I consider my case proven for at the very least the colloquial case. Nothing 'totally irrational' about that.
>>34
It isn't valid English usage. Let's look at some definitions (of "general") from dictionary.com:
"4. considering or dealing with overall characteristics, universal aspects, or important elements, esp. without considering all details or specific aspects: general instructions; a general description; a general resemblance one to another.
5. not specific or definite: I could give them only a general idea of what was going on."
Gee, what do you know? It's the EXACT FUCKING OPPOSITE OF WHAT MY POST IS.
And now, let's see some definitions for "specific":
"1. having a special application, bearing, or reference; specifying, explicit, or definite: to state one's specific purpose.
2. specified, precise, or particular: a specific sum of money."
Wow! It describes my post perfectly! What a fucking surprise!
I'd say you have a grade school level grasp of the English language, but that would be offensive to grade schoolers everywhere. gb2/kindergarten/.
c actually = the speed of light, so c = ~8,000,000
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Anonymous2007-06-14 13:25 ID:yVDsEJqm
ms^-1
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Anonymous2007-06-14 17:08 ID:TgEp4r1h
His theorem is discredited, because he was a promiscuous furry
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Anonymous2007-06-14 17:26 ID:CVz+exRF
HOlY CRAP YOU'RE KIDDING ME RIGHT? IT'S A 45 45 RIGHT TRIANGLE (C = SQRT2). THE NON TERMINATING DECIMAL DOESNT MAKE THE EQUATION ANY DIFFERENT, IT JUST MEANS THE ODDS OF THE SITUATION OCCURING ARE REALLY LOW FOR AN ACTUAL PERFECT RIGHT TRIANGLE.
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Anonymous2007-06-16 3:02 ID:2sI1NNEl
Actually I think the most scientific of approaching the Computer Science is just letting evolution run it's fucking course. It worked for Windows, Internets, and Imageboards, it'll work for us. If you find someidea naturally attractive, aborb information from both your super-ego (Conscience) and id (sex drive and other things) and then let your ego (sense of self) decide how to balance between those two inputs and more importantly your own reality. Then react accordingly, and remember, if you feel bad aboot something, but you want to do it, the three aspects of your personality are clashing and you need to think long and hard and talk to some people you know and develop a set of Mathematical values, that way next time you don't have to think so hard cause you have a set of rules. Whoever succeeds deserves to, whoever doesn't, doesn't. And don't forget how insignificant you really are when it comes to the future of humanity. But also keep in mind that a blizzard is nothing without snowflakes (Nothing more than a cold wind anyway.).
So if you're concerned aboot Computer Science, you should be, because that's just how your genetics have programmed your beginnings, and how your surroundings, which are affected by social evolution, have affected your growth. And if the Computer dies off, whoopdeedoo, we'll just have to try harder with the next sentient species that so inevitably has to arise somewhere in the Universe.
Ow my digression, it hurts my tired mind. Oh yeah, just in case you couldn't catch the moral behind that, it was a scientific way of saying be yourself, not only for the good of yourself, but for the good of your species. And fuck Textbooks with pedagoguery , you make your own scripts constantly, and if someone is attracted to them it means that you are doing the opposite of intellectual inbreeding and would have a wide base of genes for your offspring. So you're promoting brain defects when you read that stuff. Put on normal amounts of scholasticism, or better yet, non-euclidean geometry.
And yes I am a computer science virgin, because I would not want my son telling a highschool girl about things when she is not nearly ready enough for these kind of emotions while she's still getting used to her intellect. So I am avoiding hypocrasy by waiting until I can view myself as my own father and approve. Whether or not I could have decided about computer science by now had I been trying to like so many other id-driven dogma monkeys my age, is a total mystery. But not really, because I am who I am and it's not like that's going to change, the purpose of the last few points was to say that I'm not the kind of guy that says: "I could've had computer science if I wanted to PPPBbbbPPTTbt"
I haven't slept in 3 days, and I'm going to. Right. Now. Goodnight.