# Math Help - Combining chained inequalities

1. ## Combining chained inequalities

I've written a proof which ends with the (simplified) statement:

"Statement A is true iff a<x<b OR b<x<a"

This is because b is not necessarily greater than a. In plain English, "Statement A is true if and only if x is between values a and b"

I wonder if there is some way of combining the chained inequalities, hence being able to get rid of OR.

Many thanks

2. You could say, min(a,b) < x < max(a,b) or maybe x = at + b(1 - t) for some 0 < t < 1 if a and b are real numbers. Probably the simplest way is what you said, x is between a and b.

3. Originally Posted by sevenquid
I've written a proof which ends with the (simplified) statement: "Statement A is true iff a<x<b OR b<x<a"
I have just returned from a St. Patrick’s Day party (late of course). Why do Anglicans have such parties? I guess an Irish family name makes it OK.
Anyway, having time on my hands having been dragged there by my wife, I thought about this question. Again, it just popped into the ole brain with the help of Guinness.
Do it with a distance function. $c$ is between $a~\&~b$ if and only if $a,~b,~\&~c$ are three numbers such that $|a-b|=|a-c|+|c-b|.$