# Positive Integer

### Some articles on positive integer, positive, positive integers:

Properties - Continuation To Complex Values - Upper Incomplete Gamma Function
... When s is a non-positive integer in the above equation, neither part of the difference is defined, and a limiting process, here developed for s → 0, fills in the missing ... definition of, one obtains (assume x,s positive reals for now) or which, as a series representation of the entire function, converges for all complex x (and all complex s not a non-positive integer) ... of the recurrence relation, values of for positive integers n can be derived from this result, so the upper incomplete gamma function proves to exist and be holomorphic, with ...
Beatty Sequence - Rayleigh Theorem - First Proof
... We must show that every positive integer lies in one and only one of the two sequences and ... k/s when they are jointly listed in nondecreasing order for positive integers j and k ... Conclusion every positive integer (that is, every position in the list) is of the form or of the form, but not both ...
Finite Group - Number of Groups of A Given Order
... Given a positive integer n, it is not at all a routine matter to determine how many isomorphism types of groups of order n there are ... For every positive integer n, most groups of order n are solvable ... For any positive integer n there are at most two simple groups of order n, and there are infinitely many positive integers n for which there are two non-isomorphic ...
Monogenic Semigroup - Structure
... In the latter case let m be the smallest positive integer such that a m = a x for some positive integer x ≠ m, and let r be smallest positive integer such that a m = a m + r ... The positive integer m is referred to as the index and the positive integer r as the period of the monogenic semigroup ... The pair ( m, r ) of positive integers determine the structure of monogenic semigroups ...
Dimensional Regularization
... dimension of spacetime, which is a fixed positive integer (such as 4) ... The reason is that if d happens to be a positive integer, then the formula for the dimensionally regularized integral happens to be correct for spacetime of dimension d ... of a unit (d − 1)-sphere is where Γ is the gamma function when d is a positive integer, so in dimensional regularization it is common to say that this is the volume of a sphere in ...

### Famous quotes containing the word positive:

If all political power be derived only from Adam, and be to descend only to his successive heirs, by the ordinance of God and divine institution, this is a right antecedent and paramount to all government; and therefore the positive laws of men cannot determine that, which is itself the foundation of all law and government, and is to receive its rule only from the law of God and nature.
John Locke (1632–1704)