Search results
Results from the WOW.Com Content Network
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
For example, multiplying the lengths (in meters or feet) of the two sides of a rectangle gives its area (in square meters or square feet). Such a product is the subject of dimensional analysis. The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4.
Multiplication symbols are usually omitted, and implied, when there is no operator between two variables or terms, or when a coefficient is used. For example, 3 × x 2 is written as 3x 2, and 2 × x × y is written as 2xy. [5] Sometimes, multiplication symbols are replaced with either a dot or center-dot, so that x × y is written as either x ...
Here the underlying set of elements is the set of prime factors of n. For example, the number 120 has the prime factorization =, which gives the multiset {2, 2, 2, 3, 5}. A related example is the multiset of solutions of an algebraic equation. A quadratic equation, for example, has two solutions. However, in some cases they are both the same ...
An important special case is when the index set is , the natural numbers: this Cartesian product is the set of all infinite sequences with the i-th term in its corresponding set X i. For example, each element of ∏ n = 1 ∞ R = R × R × ⋯ {\displaystyle \prod _{n=1}^{\infty }\mathbb {R} =\mathbb {R} \times \mathbb {R} \times \cdots } can ...
The formula calculator concept can be applied to all types of calculator, including arithmetic, scientific, statistics, financial and conversion calculators. The calculation can be typed or pasted into an edit box of: A software package that runs on a computer, for example as a dialog box. An on-line formula calculator hosted on a web site.
This calculator program has accepted input in infix notation, and returned the answer , ¯. Here the comma is a decimal separator. Here the comma is a decimal separator. Infix notation is a method similar to immediate execution with AESH and/or AESP, but unary operations are input into the calculator in the same order as they are written on paper.
In set theory, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) —where a ∈ A and b ∈ B. [5] The class of all things (of a given type) that have Cartesian products is called a Cartesian ...