Prove that if \[\lim_{x\to a}\,(f(x)-L)=0,\] then \[\lim_{x\to a}\,f(x)=L.\]

Problem: 

Prove that if \[\lim_{x\to a}\,(f(x)-L)=0,\] then \[\lim_{x\to a}\,f(x)=L.\]

Answer: 

It is true that if \[\lim_{x\to a}\,(f(x)-L)=0,\] then \[\lim_{x\to a}\,f(x)=L.\]