increasea

Increasea is a neologism used in several informal contexts to denote a concept related to increases in a quantity. There is no universally accepted definition, and different communities have proposed different interpretations.

Etymology: The term combines the English word increase with the suffix -a; it has appeared mainly in online discussions, blogs, and speculative writings rather than in formal scholarship.

Definitions and uses: In mathematics, Increasea can denote an operator on finite sequences that extracts the positive increments between consecutive terms: for a sequence a1, a2, ..., an, Increasea(a) yields the sequence (max(0, a2−a1), max(0, a3−a2), ..., max(0, an−a_{n-1}). The initial term may be included depending on convention.

In economics and data analysis, Increasea is used as a growth-acceleration indicator, often described as a dimensionless measure of how quickly a quantity is increasing. Discrete implementations include the approximate rate of change per period, ΔQ/(Q Δt), or the change in the growth rate r_t−r_{t-1} where r_t=ΔQ/Q_{t-1}.

Examples: For the sequence 3, 5, 6, 6, 9, the Increasea increments are 2, 1, 0, 3. In growth analysis, if Q grows from 100 to 110 in one period and then to 132 in the next, the simple discrete Increasea values would reflect a rise in the growth rate, illustrating acceleration.

Variants and usage notes: Some writers coin Increasea-index or Increasea-coefficient for a normalized or smoothed version, and definitions may differ across sources. No formal standard exists.

See also: Growth rate, Acceleration, First differences, Second differences, Rate of change.