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In the mathematical subject of geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of length n.
1. The domain is the real line .The set-family contains all the half-lines (rays) from a given number to positive infinity, i.e., all sets of the form {>} for some .For any set of real numbers, the intersection contains + sets: the empty set, the set containing the largest element of , the set containing the two largest elements of , and so on.
For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ. For any non-zero time τ the growth rate is given by the dimensionless positive number b. Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different base.
The growth rate of a group is a well-defined notion from asymptotic analysis. To say that a finitely generated group has polynomial growth means the number of elements of length at most n (relative to a symmetric generating set) is bounded above by a polynomial function p(n). The order of growth is then the least degree of any such polynomial ...
Economic growth, the increase in value of the goods and services produced by an economy; Compound annual growth rate or CAGR, a measure of financial growth; Population growth rate, change in population over time; Growth rate (group theory), a property of a group in group theory
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
The asymptotic growth of the coefficients of this generating function can then be sought via the finding of A, B, α, β, and r to describe the generating function, as above. Similar asymptotic analysis is possible for exponential generating functions; with an exponential generating function, it is a n / n !
Relative growth rate (RGR) is growth rate relative to size - that is, a rate of growth per unit time, as a proportion of its size at that moment in time. It is also called the exponential growth rate, or the continuous growth rate.