- #1

Tom Mattson

Staff Emeritus

Science Advisor

Gold Member

- 5,500

- 8

Assume the following:

[tex]\lim_{\substack{x\rightarrow c}} f(x)=L_1[/tex]

[tex]\lim_{\substack{x\rightarrow c}} f(x)=L_2[/tex]

Now consider the following:

[tex]\lim_{\substack{x\rightarrow c}} f(x)+\lim_{\substack{x\rightarrow c}} f(x)=L_1 + L_1[/tex]

[tex]\lim_{\substack{x\rightarrow c}} f(x)+\lim_{\substack{x\rightarrow c}} f(x)=L_1 + L_2[/tex]

Now subtract the second equation from the first to obtain:

[tex]0=L_1-L_2[/tex]

[tex]L_1=L_2[/itex]

Therefore, the limit is unique.

Can you spot the flaw in the argument?