# Minimum-so-far

From Number

## Definition

Suppose is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number is termed a **minimum-so-far** for if for all natural numbers .

## Related notions

- Strict minimum-so-far is a natural number such that for .
- Maximum-so-far is a natural number such that for all .
- Strict maximum-so-far is natural number such that for all .