Her definition of important might not coincide widi his.

"I fear our definitions coincide," Burg said quickly.

It can be shown that the two definitions coincide for inner functions.

There is also a notion of a "smooth morphism" between schemes, and the above definition coincides with it.

If R is additionally a domain then all three definitions coincide.

This definition clearly coincides with the previous one when is a periodic point.

For commutative rings the left and right definitions coincide, but in general they are distinct from each other.

In practice, these definitions often coincide, and the differences between them are more a matter of emphasis than of outright contradiction.

This abstract definition coincides with the one in linear algebra.

However, for self-adjoint operators, all the above definitions for the essential spectrum coincide.