Hey can anyone help me prove this problem?

Let A and B be a subsets of R and bounded above.

Let InfA=a and InfB=b.

Let C= {xy ; x belongs to A, and y belongs to B}

Prove that InfC=ab

Printable View

- Oct 2nd 2012, 07:45 AMsalmasterHelp with real analysis/advanced calculus
Hey can anyone help me prove this problem?

Let A and B be a subsets of R and bounded above.

Let InfA=a and InfB=b.

Let C= {xy ; x belongs to A, and y belongs to B}

Prove that InfC=ab - Oct 2nd 2012, 07:54 AMPlatoRe: Help with real analysis/advanced calculus
- Oct 2nd 2012, 08:02 AMjohnsomeoneRe: Help with real analysis/advanced calculus
This problem isn't true as stated.

1) I think you're intending to assume that A and B are bounded.__below__

2) Let A = {-1, 1}, B = {-1}. Then a = -1, b = -1, so ab = 1. Also C = {-1, 1}, so inf(C) = -1.

Thus inf(C) is NOT equal to ab. - Oct 2nd 2012, 08:04 AMsalmasterRe: Help with real analysis/advanced calculus
Yes I'm sorry I meant bounded below.

- Oct 2nd 2012, 08:24 AMPlatoRe: Help with real analysis/advanced calculus
- Oct 2nd 2012, 08:35 AMsalmasterRe: Help with real analysis/advanced calculus
I don't think that we are supposed to prove it with specific examples of ordered pairs for A, B, and C..

- Oct 2nd 2012, 08:45 AMPlatoRe: Help with real analysis/advanced calculus