Question

I am trying to prove something, and I’m not sure if my math is correct. Simplified down, let’s say we have:

a < b < c

d < e < f

If all of these are positive values, is it legal to do:

a*d < b*e < c*f

If so, is there a property that I can cite?

This is a homework problem, so I’m looking for pointers in the right direction if no such property exists, rather than an outright answer.

Answer 1

Yes, it’s legal. Suppose a < b < c and d < e < f. Multiplying the inequality a < b by positive d gives a*d < b*d. Since we know that d < e, we have a*d < b*d < b*e. Similarly, since b < c and e < f, we get a*d < b*e < c*e < c*f.