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Divide By Zero
In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case. Using fraction notation, the general example can be written as \tfrac a0, where a is the dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor. That is, c = \tfrac ab is equivalent to c \cdot b = a. By this definition, the quotient q = \tfrac is nonsensical, as the product q \cdot 0 is always 0 rather than some other number a. Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy, a subtle mistake leading to absurd results. To prevent this, the arithmetic of real numbers and more general numerical structures called fields leaves division by zero undefined, and situations where division by zero might occur must be treated with care. Since any number multiplied by zero is zero, the expression ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Function
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term ''reciprocal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
