In real analysis, a branch of mathematics, a modulus of convergence is a function that tells how quickly a convergent sequence converges.
These moduli are often employed in the study of computable analysis and constructive mathematics.
If a sequence of real numbers
converges to a real number
, then by definition, for every real
A modulus of convergence is essentially a function that, given
is a convergent sequence of real numbers with limit
There are two ways of defining a modulus of convergence as a function from natural numbers to natural numbers: The latter definition is often employed in constructive settings, where the limit
may actually be identified with the convergent sequence.
Some authors use an alternate definition that replaces