Numrets

Numrets are a fictional construct used in speculative numeration theory to explore how numeral representations could be built from adaptable base systems. A numret is the basic elemental unit of a numeral, encoding a single digit together with an associated base and a positional exponent.

A numeral in this system consists of a sequence of numrets, typically ordered from most significant to least. The value of a numret is calculated as digit times base raised to the exponent, i.e., value = digit × base^exponent. Unlike fixed-base systems, the base may vary by position, enabling nonuniform positional notation and providing a framework for studying base-change and carry rules.

Key questions in numret theory include the conditions under which representations are unique, how to normalize sequences of numrets, and how conversions to standard fixed-base representations would be defined. The framework emphasizes the relationships between digit range, base variation, and numerical value.

Example: a three-numret numeral with entries (3, base=5, exp=2), (1, base=5, exp=1), (4, base=5, exp=0) yields 3×5^2 + 1×5^1 + 4×5^0 = 75 + 5 + 4 = 84.

In literature and teaching, numrets are used as a pedagogical tool to illustrate how changing bases affect representation, comparison, and conversion. They are not part of standard mathematics but serve as a provocative thought experiment and a basis for discussions of numeral systems.