Maximum-so-far

Definition

Suppose $\text{[math]}$ is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number $\text{[math]}$ is termed a maximum-so-far for $\text{[math]}$ if $\text{[math]}$ for all natural numbers $\text{[math]}$ .

Related notions

Strict minimum-so-far is a natural number $\text{[math]}$ such that $\text{[math]}$ for $\text{[math]}$ .
Minimum-so-far is a natural number $\text{[math]}$ such that $\text{[math]}$ for all $\text{[math]}$ .
Strict maximum-so-far is natural number $\text{[math]}$ such that $\text{[math]}$ for all $\text{[math]}$ .

Maximum-so-far

Definition

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