# Transformation of a region

1. May 19, 2008

### the1ceman

Hello. I am trying to work out what the region

$$\{0\leq\tau\leq t,0\leq t<\infty\}$$ Is under the transformation:

$$t=u+v,\tau=v$$

I know its just
$$\{0\leq u<\infty,0\leq v<\infty\}$$
But i am having difficulty showing this.
Thanks.

2. May 22, 2008

### the1ceman

Anyone?

3. May 22, 2008

### Defennder

$$0 \leq v \leq u+v < \infty$$ after substituting u, v for tau and t and combining the inequalities.

Subtracting v from from the above inequalities give: $$0 \leq u < \infty$$
From the first inequality you should be able to see that $$0\leq v<\infty$$ holds.

Last edited: May 22, 2008