Show that all $x$ satisfying $0\lt |x-a|\lt\delta$ is equivalent to the union $(a-\delta,a)\cup (a,a+\delta)$ where $a$ is any real number and $\delta\gt 0$.
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Lesson Parent:
Problem:
Show that all $x$ satisfying $0\lt |x-a|\lt\delta$ is equivalent to the union $(a-\delta,a)\cup (a,a+\delta)$ where $a$ is any real number and $\delta\gt 0$.
Answer:
It is true that $0\lt |x-a|\lt\delta$ is equivalent to the union $(a-\delta,a)\cup (a,a+\delta)$.
