Symmetrically continuous function

In mathematics, a function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is symmetrically continuous at a point x if lim h → 0 f ( x + h ) − f ( x − h ) = 0. {\displaystyle \lim _{h\to 0}f(x+h)-f(x-h)=0.} The usual definition of continuity implies symmetric continuity, but the converse is not true.

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