Question: How does the transformation of a region affect its boundaries?

[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.

 

[the1ceman]

Anyone?

 

[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.