A function is said to besymmetrically continuousat if

Show that if is continuous at , it is symmetrically continuous there but not the conversely.

Printable View

- Mar 14th 2010, 06:16 AMyusukered07Symmetrically Continuous
A function is said to be

**symmetrically continuous**at if

Show that if is continuous at , it is symmetrically continuous there but not the conversely. - Mar 14th 2010, 12:03 PMTinyboss
The forward direction is trivial--just use the fact that the limit of the difference is the difference of the limits, together with the limit definition of continuity.

Disproving the converse is almost as easy--just consider

.