Strict minimum-so-far: Difference between revisions

Latest revision as of 18:39, 2 May 2009

Definition

Suppose $f$ is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number $n$ is termed a strict minimum-so-far for $f$ if $f (n) < f (m)$ for all natural numbers $m < n$ .

Related notions

Minimum-so-far is a natural number $n$ such that $f (n) \leq f (m)$ for $m \leq n$ .
Maximum-so-far is a natural number $n$ such that $f (m) \leq f (n)$ for all $m \leq n$ .
Strict maximum-so-far is natural number $n$ such that $f (m) < f (n)$ for all $m < n$ .

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 ==Definition==
-Suppose <math>f</math> is an arithmetic function from the [[natural number]]s to a subring of the ring of real numbers. Then, a [[natural number]] <math>n</math> is termed a '''minimum-so-far''' for <math>f</math> if <math>f(n) < f(m)</math> for all natural numbers <math>m < n</math>.
+Suppose <math>f</math> is an arithmetic function from the [[natural number]]s to a subring of the ring of real numbers. Then, a [[natural number]] <math>n</math> is termed a '''strict minimum-so-far''' for <math>f</math> if <math>f(n) < f(m)</math> for all natural numbers <math>m < n</math>.
 ==Related notions==