User:CompactStar/Super-pitch: Difference between revisions
CompactStar (talk | contribs) Created page with "(Would have created in mainspace, but this is WIP and the explanation is currently somewhat vague) '''Super-pitch''' is a quantity that is equal to the [https://en.wikipedia...." |
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For example, slog<sub>b</sub>(b) = 1, slog<sub>b</sub>(b<sup>b</sup>) = 2 and slog<sub>b</sub>(b<sup>b<sup>b</sup></sup>) = 3. Super-logarithms are only defined for inputs that are a power tower of the base (1, b, b<sup>b</sup>, b<sup>b<sup>b</sup></sup>, etc.). However, there are various generalizations of the super-logarithm to other inputs, the most common of which is the linear approximation, defined as: | For example, slog<sub>b</sub>(b) = 1, slog<sub>b</sub>(b<sup>b</sup>) = 2 and slog<sub>b</sub>(b<sup>b<sup>b</sup></sup>) = 3. Super-logarithms are only defined for inputs that are a power tower of the base (1, b, b<sup>b</sup>, b<sup>b<sup>b</sup></sup>, etc.). However, there are various generalizations of the super-logarithm to other inputs, the most common of which is the linear approximation, defined as: | ||
slog<sub>b</sub>(x) = x - 1 if 0 & | slog<sub>b</sub>(x) = x - 1 if 0 ≤ x ≤ l | ||
slog<sub>b</sub>(b<sup>x</sup>) = slog<sub>b</sub>(x) + 1 | slog<sub>b</sub>(b<sup>x</sup>) = slog<sub>b</sub>(x) + 1 | ||