Recent content by SMG75

I'm mostly confused by b>z-x in your post. Can you explain why that is true?

Yes, I follow until there. I'm not sure how I prove that, though...

I think I was following well until this point, but now I'm totally lost. Would you mind explaining this? By the way, I really appreciate the help.

I'm a little stuck in thinking about this. Intuitively, I know a is the least upperbound of A by definition, and b is the least upperbound of B, similarly. Having a least upperbound of A+B greater than a+b implies that either a or b was not a least upperbound to begin with. I'm not sure where...

Well, since x\inA, it is by definition less than a, which is the upperbound of A. Similarly, y is less than b. Therefore, x+y\leqa+b. I'm not sure how to formalize this intuition, though.

Can anyone tell me if I'm on the right track here?

The part that says \left and \right is supposed to be absolute value. I'm not sure how to input that.

Let A_{w}=set of whole parts of elements of A+B A_{w} is bounded from above because A+B is bounded. Let a_{w}=max(A_{w}. And let A_{1} \subseteq A+B be the subset of A+B containing all elements that begin a_{w}. ...(decimal expansion). Assume a_{w} \geq 0. Let a_{1}=max (1/10)'s digit of...

That makes perfect sense, actually. Where should I go from here?

If S is a nonempty subset of numbers, then M=sup(S) if and only if M is an upperbound for S AND for any z>0, M-z is not an upperbound for S. Is this a solid definition?

I suppose saying I have no clue where to start was a bit of an overstatement. a is not only the upperbound of A but the smallest possible upperbound. Same for b/B. This is the definition of a supremum. When the sets are added together, the supremum of that new set, call it C, is the same...

Homework Statement Suppose a = sup(A) and b = sup(B). Let A + B = \left\{x + y;x\inA; y\inB\right\}. Show that a + b = sup(A + B). Homework Equations The Attempt at a Solution I'm honestly not sure where to start. Any help guys?

Homework Statement Suppose x, y \in\Re^{n} are nonparallel vectors. a) Prove that if sx+ty=0, then s=t=0 b) Prove that if ax+by=cx+dy, then a=c and b=dHomework Equations The Attempt at a Solution I'm very new to proof-based math, so I'm just trying to get my feet wet here. I realize this is a...

Hey all, I have a pretty solid background in what would be best described as applied or engineering math. However, I have had a very limited exposure to proofs. This fall, I will be taking a course covering linear algebra and vector calculus in an entirely proof-based manner. I'm looking...

Thank you very much guys! Your replies were quite helpful.