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The set of all point $x$ such that $|x-a| < \delta$ is called a $\delta$ neighborhood of the point $a$. The set of all points $x$ such that $0<|x-a|<\delta$ in which $x=a$ is excluded, is called a deleted $\delta$ neighborhood of $a$ or an open ball radius $\delta$ about $a$.

I don't understand this definition (and because of that also the definition of a limit point):

  • Is $\delta$ just a random positive integer?

  • What exactly is the use of a $\delta$ neighborhood, I don't see how it could be meaningful at all.

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    Have you ever worked with limits?2012-12-01
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    @use Only with basic calculus, not much.2012-12-01

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