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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.

Proofs: 1


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References

Bibliography

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