Branches History Index

◀ ▲ ▶Branches / Analysis / Proposition: Limit of a Function is Unique If It Exists

Proposition: Limit of a Function is Unique If It Exists

Let $D\subseteq\mathbb R$ be a subset of real numbers and let $f:D\to\mathbb R$ be a function having the limit $L$ at $x=a\in D$. Then this limit is unique. Formally $$\lim_{x\to a} f(x)=L\wedge \lim_{x\to a} f(x)=M\Longrightarrow L=M.$$

Table of Contents

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs

References

Bibliography

  1. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016