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Cornell's fractals group is done. I got an email this morning at 7:30am saying that the first people to respond to the email would be an offered a spot on the project. I did not see the email until 3pm today when the group was already filled, and as I have already accepted a position on...

Apparently Cornell will not be receiving word from the NSF about their funding until the end of this week or beginning of next week, and thus, will not be sending out any offers until around that time. I too have an offer from CSUCI and need to respond by Friday. It looks like I will be...

Yeah, because clearly the fact that due dates are staggered necessitates that you stagger your submissions.

I think vrdfx wasn't asking how -|x|<x<|x| + -|y|<y<|y| = -|x|-|y|<x+y<|x|+|y| => -(|x|+|y|)<x+y<|x|+|y| , but how -(|x|+|y|)<x+y<|x|+|y| yields |x+y|<|x|+|y|. Does -(|x|+|y|) = |x+y| or something? I don't see how it could...

Homework Statement Help with either of these problems would be great. 1. Suppose R is a partial order on A and B\subseteq A. Prove that R \cap \left(B\times B\right) is a partial order on B. 2. Suppose R1 is a partial order on A1, R2 is a partial order on A2, and A_1 \cap A_2 = \emptyset...

How would I be able to prove that using the triangle inequality? I thought that the answer would be something along the lines of |x-z|< r and s or something like that... I know that is the "answer" but I thought the answer would be more... numerical. Maybe I just totally misunderstood what...

I'm using Velleman's "How to Prove it" and I'm doing this self study. I suppose I am having some trouble understanding some of these definitions. I guess I will just have to re-read a few chapters... Could you just tell me what D_s \circ D_r would be? Maybe then I would understand how it...

no. I'm still not really following though. I just cannot figure out how to combine the two relations to create a composition. =/

I have been using the definition, and I still have no idea what D_s \circ D_r would be. I just don't understand how you can use composition with two relations over the same elements. If one of them were (x,y) and the other one were (y,z) then I might be able to figure this out on my own.

I've read everything my book has to say about the composition of relations, and I cannot figure out what to do with this problem. With the other problems, it would just say, for example, that A was a relation from X to Y and B was a relation from Y to Z, then the composition of B and A would be...

Homework Statement Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is D_r \circ D_s? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.) Homework Equations Example 4.3.1...

new problem bump

Homework Statement I originally made this thread for something else, but I have another problem that I need help with. Suppose a and b are nonzero real numbers. Prove that if a < 1/a < b < 1/b then a < -1. Homework Equations A hint was given for the problem: Assume a < 1/a < b <...

Ah, okay. I guess I was stuck thinking that (x,y) was in R and didn't consider that R being symmetric could mean that if yRx then xRy. And yes, R was a relation haha. Thanks!

Homework Statement In Velleman's "How to Prove it", he gives a proof that "R is symmetric iff R = R-1, which I find to be confusing when he is proving that R^{-1}\subseteq{R}: Now suppose (x,y)\in R^{-1}. Then (y,x)\in R, so since R is symmetric, (x,y)\in R. Thus, R^{-1}\subseteq R so R=R-1...