How to Prove Points in an Open Interval are of a Certain Form?

[JG89]

Homework Statement

Prove the points of the open interval (a,b) are those of the form a + t(b-a) for 0 < t < 1.

Homework Equations

The Attempt at a Solution

I'm interpreting this as asking me to prove that if x is in (a,b), then x can be written as
a + t(b-a) for some 0 < t < 1. Conversely, it's asking me to prove that if x = a + t(b-a) with 0 < t < 1, then x is in (a,b).

Is this interpretation correct?

 

[JG89]

Please answer quick. This is a homework question due in a couple hours. I've already finished the question and my problem set, but I want to make sure that I proved the correct thing!

 

[HallsofIvy]

Yes, your interpretation is correct.

Sorry I couldn't get this to you sooner but I was busy with something I am actually paid to do.

 

[JG89]

but I was busy with something I am actually paid to do.

I'll pay you double! Just kidding, thanks for the response. It came in time :)