- #1

kathrynag

- 598

- 0

## Homework Statement

For a,b elements of the real numbers, define a~b if [tex]\left|a-b\right|[/tex][tex]\leq[/tex]

1. Determine if we have an equivalence relation.

## Homework Equations

## The Attempt at a Solution

I've already done the first two parts of determining. it's only the last part that I'm having trouble with, so i will omit the first two parts.

We bwant to determine if for all a,b,c elements of S, if (a,b) is an element of R and (b,c) is an element of R, then (a,c) is an element of R.

We know [tex]\left|a-b\right|[/tex][tex]\leq[/tex]1 and [tex]\left|b-c\right|[/tex][tex]\leq[/tex]1.

This means a-b[tex]\leq[/tex]1,b-a[tex]\leq[/tex]1, b-c[tex]\leq[/tex]1, and c-b[tex]\leq[/tex]1.

Furthermore, a[tex]\leq[/tex]1+b, b[tex]\leq[/tex]1+a, b[tex]\leq[/tex]1+c, c[tex]\leq[/tex]b+1.

I know from this, I need to be able to show a-c[tex]\leq[/tex]1 and c-a[tex]\leq[/tex]1 in order to have an equivalence relation.

That's what I don't see right off hand is how to get that.