Vipul: Created page with '==Definition== Suppose $f$ is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number $n$ ...'

2009-05-02T18:41:21Z

Created page with '==Definition== Suppose <math>f</math> is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number <math>n</math> ...'

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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 '''strict maximum-so-far''' for <math>f</math> if <math>f(n) > f(m)</math> for all natural numbers <math>m < n</math>.

==Related notions==

* [[Strict minimum-so-far]] is a natural number <math>n</math> such that <math>f(n) < f(m)</math> for <math>m < n</math>.
* [[Maximum-so-far]] is a natural number <math>n</math> such that <math>f(m) \le f(n)</math> for all <math>m \le n</math>.
* [[Minimum-so-far]] is natural number <math>n</math> such that <math>f(m) \ge f(n)</math> for all <math>m \le n</math>.

Strict maximum-so-far - Revision history

Vipul: Created page with '==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 ...'

Vipul: Created page with '==Definition== Suppose $f$ is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number $n$ ...'