Concept of equality conditional to existence of one side

From Calculus
Jump to: navigation, search

General concept

There are a number of theorems in mathematics which are of the following form:

\mbox{Left side expression} = \mbox{Right side expression}

with a conditionality caveat as follows:

  • Whenever the right side expression makes sense, the left side expression also makes sense and they are equal.
  • It may, however, happen that the right side expression does not make sense but the left side expression does.

This concept occurs in theorems about limits and derivatives of pointwise combinations (sums, differences, products, quotients), as well as composites.