Pythagoras

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?  

Obviously talking about right triangles here...

>>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.

>>3
More specifically, if N is a positive integer and sqrt(N) is not an integer, than sqrt(N) is irrational.

thanks for the info guys... this was bugging me.

That's not more specifically, that's more in general.

>>6
He gave a list with no immediately obvious extension (3, 5, 6, 7..), and I *specified* the the entire list.

>>7

No, you generalized the list to a bigger one.

This question is bullshit

>>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.

>>10
He gave 4 specific examples, you gave a general rule.
Guess I have no idea 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/.

A GENERAL rule that SPECIFIES which numbers belong to the set, now STFU.

A GENERAL rule that SPECIFIES which numbers belong to the set, now STFU.

oops :)

>>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)

Notice how I didn't fucking use it.

LAFFO math fight

LAFFO diction fight

-fixed

>>16


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.

>>19
Funny you should mention this definition:

"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."

Because I did neither of those things.

I can't believe how stupid this argument is.

LAFFO

You are really fucking slow, man. (btw, I'm a new poster.)

This is basically what happened, with some fun names added:

Alice: Most roots of naturals are irrational. Root 3, 5, 6, 7, etc.

Bob: More specifically, if N is a positive integer and sqrt(N) is not an integer, than sqrt(N) is irrational.

Alice decided to say that "most" roots of natural numbers are irrational, and then gave the example of 3, 5, 6 and 7.

Bob then generalised this statement into one which goes along the lines of: unless N is a square number, sqrt(N) is irrational.

One is a more generalised statement of the other.

>>23
"There exist elements with property P"

"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.

"general case" surely you have heard of such a thing - you specified the general case, LOLz

>>10
Nice ad hominem argument.

From Wikipedia:

<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".


Thread over?

>>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
Whoops, >>27 here. Forgot my sage.

>>28
You're welcome to stand by your claim, but it makes you look like a toothpaste.

(FYI, toothpaste means moron, and I'm just going to continue saying such in the face of all evidence to the contrary.)

>>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.

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.

>>33
idiot

>>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/.

>>32
mm  lol

>>1
1+1=2
2^0.5=c

c actually = the speed of light, so c = ~8,000,000

ms^-1