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Other symbols for division include the slash or solidus /, the colon:, and the fraction bar (the horizontal bar in a vertical fraction). [3] [4] The ISO 80000-2 standard for mathematical notation recommends only the solidus / or "fraction bar" for division, or the "colon" : for ratios; it says that the ÷ sign "should not be used" for division. [1]
This division sign is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator. The obelus was introduced by Swiss mathematician Johann Rahn in 1659 in Teutsche Algebra. [10]: 211 The ÷ symbol is used to indicate subtraction in some European countries, so its use may be misunderstood. [11]
See History of algebra: The symbol x. 1637 [2] René Descartes (La Géométrie) √ ̅ . ... 1684 (deriving from use of colon to denote fractions, dating back to 1633
2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
An example of long division performed without a calculator. A more detailed breakdown of the steps goes as follows: Find the shortest sequence of digits starting from the left end of the dividend, 500, that the divisor 4 goes into at least once. In this case, this is simply the first digit, 5.
In abstract algebra, if I and J are ideals of a commutative ring R, their ideal quotient ... (I : J) is sometimes referred to as a colon ideal because of the notation.
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The vertical bar (or colon) is a separator that can be read as "such that", "for which", or "with the property that". The formula Φ(x) is said to be the rule or the predicate. All values of x for which the predicate holds (is true) belong to the set being defined.