Reciprocals of Intervals Question

[cmajor47]

Homework Statement

I had a question about intervals and their reciprocals. If you have the reciprocal I where I is [r,s] than the reciprocal is [1/s , 1/r]. My question is when an interval contains zero, does the interval have a reciprocal. For instance if J is the interval [-2,7] does J have a reciprocal, and if so what is the formula for finding it?

Homework Equations

I = [r,s]
1/I = [1/s , 1/r]

The Attempt at a Solution

 

[HallsofIvy]

Please give the specific definition of "reciprocal" of an interval you are using. So far all you have said is that the reciprocal of [r, s] is [1/s, 1/r] which appears to be an example rather than a definition. If that really is the definition then it would appear that "reciprocal" of an interval depends ony on the endpoints and has nothing to do with points in its interior. But in that case, you appear to be saying that the reciprocal of [-2, 7] is [1/7, -1/2] which can't be true because 1/7> -1/2.