Math Is Fun Forum

hahaha, there are two guys i can think of at my school that only passed math 171 and 271 (calc II and III) because they had a fancy calculator. I said it looks like the number associated with the course (171, 271) corresponds to the cost (in dollars) of the calculator they need to pass the course.

So I guess it does enable you to pass in some exams or quizzes, but... definitely you're setting yourself up for failure in the very near future. (probably in the next subsequent course)

Okay, but does that mean vectors in R^n/ C^n, or does it deal with the elements of any vector space?

Seems to me you should be able to develop a calculus for any vector space over a Field that contains an infinite number of elements between a and b...

um.. no? Multiplying both dies of  1/3=0.333 gives you 1 = 0.999..." which says they are equal. It does not say they are unequal. So how would that suggest they are unequal?

Proof by example works usually to show that something is not true in all cases. For instance, prove that not all quadratic equations have two unique roots. You can prove this by taking the example of x^2 -4x + 4 = 0, 2 is the only (real) root of this equation. Even if this happened to be the only equation without two unique roots, it would still hold that all of them don't have that.

As for backwards proofs, you have to be careful with which way the implication works in your logic. All dogs have 4 legs but not everything with 4 legs is a dog.  In this problem you are given a premise, equation 1 and have to show that equation 1 implies equation 2, so 1 ⇒  2 (1 implies 2) but you can't just start with 2 and show that 2 ⇒ 1.

What you can do is proof by contrapositive. In which you say suppose 2 is not true, if you can prove that 2 is false implies 1 is false, then clearly if 1 is true, then 2 must be true.

Not however, that many times when showing two equations are equivalent, you can work in both directions, but not always. You must be careful.

thanks jane, but didn't I tell you not to prove it?
fortunately,  I got that much of the proof, but that assumes initially that, given ax = 1, there is some matrix y such that ya = 1 (has a left/right inverse implies has a right/left inverse). If we can show one exists, then we can show by the above proof that they must be equal. 

I'm simply trying to prove that, if Ax = 1 implies  xA = 1.

for one, I noted Ax = 1  implies (Ax)A = A(xA) = A, but I'm not sure if AM = A implies M = I, and so the problem reduced to trying to prove that.

hahaha, I even caught my calc teacher at school making that exact mistake, marked it wrong when I said

wrote infinity in red ink. A lot of people thanked me when I pointed out that 'does not exist' was indeed the correct answer.

The two sided rule is just a technicality thats easy to forget. Just an honest mistake, not bs. Did you get enough sleep, Jane?

this post made me laugh.

hahahaha, that guy is one of a kind!

Thanks for the response!

Yes, I've noticed makefile's typically appear. I opened the readme of a particular library and it gives instructions for Unix installation, and says the process can be emulated for mac or windows. Not sure what that means, though.

In any case, configure, make, and make install. Can you tell me where I can learn how to perform these three steps?

I really know very little about command line processing, which I think is what this is.

While we're on the subject of science and oral health, has anyone else heard the claim that Fluoride, an ingredient commonly used in toothpaste that is supposed to strengthen your teeth, actually does no such thing? Many conspiracy theorists seem to endorse this notion, and I've often wondered if there's any truth to it.