# Treatment of Inequalities

I've been playing around with some proofs and find myself relearning how I do my mathmatical thinking. Just a general question regarding how to handle something like this.

0<a<b So a and b must be positive
a/2 <b I just divided one side by two instead of "dividing through" like you would an equation. The statement is still true, would this be a legal manipulation (for whatever reason)?

Char. Limit
Gold Member
I've been playing around with some proofs and find myself relearning how I do my mathmatical thinking. Just a general question regarding how to handle something like this.

0<a<b So a and b must be positive
a/2 <b I just divided one side by two instead of "dividing through" like you would an equation. The statement is still true, would this be a legal manipulation (for whatever reason)?
Well, you might have to justify it, but it's still certainly true, because for positive b:

b/2 < b

And by dividing all sides of the equation by 2, you get...

0<a/2<b/2<b --> 0<a/2<b