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Gijswijt's sequence is known for its remarkably slow rate of growth. For example, the first 4 appears at the 220th term, and the first 5 appears near the 10 10 23 {\displaystyle 10^{10^{23}}} rd term.
The slow-growing hierarchy grows much more slowly than the fast-growing hierarchy. Even g ε 0 is only equivalent to f 3 and g α only attains the growth of f ε 0 (the first function that Peano arithmetic cannot prove total in the hierarchy) when α is the Bachmann–Howard ordinal.
The right-most column shows a projection for the time period shown using the medium fertility variant. Preceding columns show actual history. The number shown is the average annual growth rate for the period.
The population in some of the largest cities in America has been declining as Americans flee to smaller cities with more affordable living costs. Of the 10 most populous U.S. cities, four saw...
Most of this year’s software companies are business-to-business firms. Cybersecurity and programming support systems are a major presence, with collaborationsoftware maker Atlassian occupying ...
It is related to the fast-growing hierarchy and slow-growing hierarchy. Hardy hierarchy is introduced by Stanley S. Wainer in 1972, [ 1 ] [ 2 ] but the idea of its definition comes from Hardy's 1904 paper, [ 2 ] [ 3 ] in which Hardy exhibits a set of reals with cardinality ℵ 1 {\displaystyle \aleph _{1}} .
Or maybe you’ve seen bald spots slowly grow bigger over the years. You’re certainly not alone. Androgenetic alopecia or androgenic alopecia — the medical term for male pattern baldness ...
The fast-growing hierarchy, Hardy hierarchy, and slow-growing hierarchy of functions are all defined via a chosen system of fundamental sequences up to a given ordinal. The fast-growing hierarchy is closely related to the Hardy hierarchy, which is used in proof theory along with the slow-growing hierarchy to majorize the provably computable ...