# Thread: THEORY: Why the definition of limit requires an open interval?

1. ## THEORY: Why the definition of limit requires an open interval?

Hello,

although I understand what limit is about I don't understand why the definition requires an interval like this

$\displaystyle \left ( a,p \right )\cup \left ( p,b \right )$

and not one like this:

$\displaystyle \left [ a,p \right )\cup \left ( p,b \right ]$

when it wants to show that there exists the limit on the point p. How the second one would harm the limit definition?

2. ## Re: THEORY: Why the definition of limit requires an open interval?

Originally Posted by Melsi
$\displaystyle \left ( a,p \right )\cup \left ( p,b \right )$ and not one like this: $\displaystyle \left [ a,p \right )\cup \left ( p,b \right ]$
It is irrelevant. In both cases, the function is defined for points sufficiently close to $\displaystyle p$, so it has sense to study the behavior of $\displaystyle f(x)$ as $\displaystyle x\to p$ . Limit is a local concept.

3. ## Re: THEORY: Why the definition of limit requires an open interval?

Originally Posted by Melsi
Hello,

although I understand what limit is about I don't understand why the definition requires an interval like this

$\displaystyle \left ( a,p \right )\cup \left ( p,b \right )$

and not one like this:

$\displaystyle \left [ a,p \right )\cup \left ( p,b \right ]$

when it wants to show that there exists the limit on the point p. How the second one would harm the limit definition?