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In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
The word "formal" indicates that the series need not converge. In mathematics, and especially in algebra, a formal series is an infinite sum that is considered independently from any notion of convergence and can be manipulated with algebraic operations on series (addition, subtraction, multiplication, division, partial sums, etc.).
Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term). mathematics See mathematics. multivalued A "multivalued function” from a set A to a set B is a function from A to the subsets of B.
The product of non-negative integers can be defined with set theory using cardinal numbers or the Peano axioms. See below how to extend this to multiplying arbitrary integers, and then arbitrary rational numbers. The product of real numbers is defined in terms of products of rational numbers; see construction of the real numbers. [32]
In mathematics, a multiple is the product of any quantity and an integer. [1] In other words, for the quantities a and b, it can be said that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that / is an integer.
The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together) Outer ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second) Inner ("inside" terms are multiplied—second term of the first binomial and first term of the ...
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. [1] In terms of set-builder notation , that is A × B = { ( a , b ) ∣ a ∈ A and b ∈ B } . {\displaystyle A\times B=\{(a,b)\mid a\in A\ {\mbox{ and }}\ b\in B\}.} [ 2 ] [ 3 ]
In fact, if we consider these as formal generating functions, the existence of such a formal Euler product expansion is a necessary and sufficient condition that a(n) be multiplicative: this says exactly that a(n) is the product of the a(p k) whenever n factors as the product of the powers p k of distinct primes p.