Unique Limits Proof

Theorem

• Let $L_1,L_2,c\in R$
• Suppose that $f$ is defined on an open interval around $c$ (except possibly at $c$)
• If ${\lim }_{x\to c}=L_1$
• If ${\lim }_{x\to c}f(x)=L_2$
• Then $L_1=L_2$.

Proof

Proof By Contradiction