Division (mathematics) | Mathematical fallacies | Infinity | Mathematical analysis | Computer arithmetic
Division by infinity
In mathematics, division by infinity is division where the divisor (denominator) is infinity. In ordinary arithmetic, this does not have a well-defined meaning, since infinity 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, gives a finite number. However, "dividing by infinity" can be given meaning as an informal way of expressing the limit of dividing a number by larger and larger divisors. Using mathematical structures that go beyond the real numbers, it is possible to define numbers that have infinite magnitude yet can still be manipulated in ways much like ordinary arithmetic. For example, on the extended real number line, dividing any real number by infinity yields zero, while in the surreal number system, dividing 1 by the infinite number yields the infinitesimal number . In floating-point arithmetic, any finite number divided by is equal to positive or negative zero if the numerator is finite. Otherwise, the result is NaN. The challenges of providing a rigorous meaning of "division by infinity" are analogous to those of defining division by zero. (Wikipedia).
