Ordinal Arithmetic
... Hint: You can define a bijection by transfinite recursion. Say something like “if x is the least element for which f is not yet defined, define f (x) to be. . . ” ...
... Hint: You can define a bijection by transfinite recursion. Say something like “if x is the least element for which f is not yet defined, define f (x) to be. . . ” ...
complex numbers and complex functions
... Now we recognize it as a complex number. Field properties. The set of complex numbers C form a field. That essentially means that we can do arithmetic with complex numbers. When performing arithmetic, we simply treat ı as a symbolic constant with the property that ı2 = −1. The field of complex numbe ...
... Now we recognize it as a complex number. Field properties. The set of complex numbers C form a field. That essentially means that we can do arithmetic with complex numbers. When performing arithmetic, we simply treat ı as a symbolic constant with the property that ı2 = −1. The field of complex numbe ...
Sums of Two Triangulars and of Two Squares Associated with Sum
... proven independently by Jacobi [8]; and the full proof of Fermat’s theorem was shown by Cauchy [9]. There are also several recent studies on the sums of triangular numbers and of squares. Farkas used the theory of theta functions to discover formulas for the number of representations of a natural nu ...
... proven independently by Jacobi [8]; and the full proof of Fermat’s theorem was shown by Cauchy [9]. There are also several recent studies on the sums of triangular numbers and of squares. Farkas used the theory of theta functions to discover formulas for the number of representations of a natural nu ...
Uniform satisfiability in PSPACE for local temporal logics over
... the set of actions the system might perform together with the dependency relation between these actions. A more concrete view of the architecture is a set of processes and a mapping from each action to the set of processes involved in this action. Here, two actions are dependent if they share a comm ...
... the set of actions the system might perform together with the dependency relation between these actions. A more concrete view of the architecture is a set of processes and a mapping from each action to the set of processes involved in this action. Here, two actions are dependent if they share a comm ...
Sequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006
... related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost p ...
... related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost p ...
Why Do All Composite Fermat Numbers Become
... It has been proved that any prime number p satisfies Fermat’s little theorem, which includes Fermat primes. But there are some composite numbers also satisfy Fermat’s little theorem, in which the smallest such composite number is 341=11×31, so that such composite numbers are called pseudoprimes to b ...
... It has been proved that any prime number p satisfies Fermat’s little theorem, which includes Fermat primes. But there are some composite numbers also satisfy Fermat’s little theorem, in which the smallest such composite number is 341=11×31, so that such composite numbers are called pseudoprimes to b ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.