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Division by zero. The reciprocal function y = 1 x. As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
The division-by-zero fallacy has many variants. The following example uses a disguised division by zero to "prove" that 2 = 1, but can be modified to prove that any number equals any other number. Let a and b be equal, nonzero quantities = Multiply by a = Subtract b 2
The hyperbola = /.As approaches ∞, approaches 0.. In mathematics, division by infinity is division where the divisor (denominator) is ∞.In ordinary arithmetic, this does not have a well-defined meaning, since ∞ is a mathematical concept that does not correspond to a specific number, and moreover, there is no nonzero real number that, when added to itself an infinite number of times ...
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...
Extraneous and missing solutions. In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not ...
Greatest common divisor. In mathematics, the greatest common divisor ( GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. [ 1][ 2]
Although ordinary division is not defined on , the division "with remainder" is defined on them. It is called Euclidean division , and possesses the following important property: given two integers a and b with b ≠ 0 , there exist unique integers q and r such that a = q × b + r and 0 ≤ r < | b | , where | b | denotes the absolute value of b .
Undefined (mathematics) In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the possibility of assuming different values). [ 1] The term can take on several different meanings depending on the context. For example: