# Left-hand limit definition

I have the following definition:

Let $$I\subseteq \Bbb R$$ be an open interval and let $$c\in I$$. A function $$f:I \setminus \{c\}\rightarrow \Bbb R$$ has a left hand limit in the point $$c$$ equal to $$L$$ if:

$$(\forall \varepsilon>0)(\exists \delta>0)(\forall x\in I)((0 Then we say that $$\lim_{x\to c^-}f(x)=L.$$

Can someone please explain this definition with an example or tell me where I can find some help on understanding this definition?

• Informally it means: no matter what size interval around L you give me (on the y axis), I can find an interval on the x axis of the form (c- something ositive, c) such that ALL the points from that interval map to something within the interval around L you gave me. – Ovi Feb 8 '17 at 17:21
• $c\in I^\circ$. – Nosrati Feb 8 '17 at 17:24

Draw the graph of $$f(x) = \left\{ \array{x & (x < 1) \\ x+1 & (x\ge 1)} \right.$$ The left hand limit of $f$ at $x=1$ is $=1$, the right hand limit (defined similarly) is $=2$