1 }, The adjective indeterminate does not imply that the limit does not exist, as many of the examples above show. = {\displaystyle \infty /0} , so L'Hôpital's rule applies to it. is particularly common in calculus, because it often arises in the evaluation of derivatives using their definition in terms of limit. α Zero is zero, or nothing. ( All the lines, however, converge on 0/0. ∞
) {\displaystyle 1} g
). f (
x But any number multiplied by 0 is 0 and so there is no number that solves the equation. {\displaystyle 0^{0}} . ) ) 0
{\displaystyle \infty /\infty } g {\displaystyle g}
β The graphical programming language Scratch 2.0 and 3.0 used in many schools returns Infinity or −Infinity depending on the sign of the dividend.
∞ For the evaluation of the indeterminate form {\displaystyle f/g} Zero divided by zero is zero. Why some people say it's 1: A number divided by itself is 1. What is 0 divided by 0? 1 A positive or negative number when divided by zero is a fraction with the zero as denominator. f
Our mission is to provide a free, world-class education to anyone, anywhere. , one of these forms may be more useful than the other in a particular case (because of the possibility of algebraic simplification afterwards). Quick sign-up, no credit card required. g {\displaystyle f'} 1 The mathematician contemplates suicide, but the story ends without any particular resolution. 1 A correspondent recently complained that the momentum of a photon is derived from its frequency and is not simple result of velocity times mass, and that zero times infinity is actually zero. . / This is enough to show that 0 {\displaystyle a=-\infty } > {\displaystyle \lim _{b\to 0}{a \over b}} means an unsigned infinity, an infinite quantity that is neither positive nor negative. {\displaystyle 0}
In the hyperreal numbers and the surreal numbers, division by zero is still impossible, but division by non-zero infinitesimals is possible. More specifically, an indeterminate form is a mathematical expression involving {\displaystyle 1} Zero times anything is zero, but then infinity times anything is infinite.
[4] Similarly, when the realm of numbers expands to include the rational numbers, division is replaced by multiplication by certain rational numbers. and (
The concepts applied to standard arithmetic are similar to those in more general algebraic structures, such as rings and fields.
∞
−
{\displaystyle 1} Each person would receive 10/5 = 2 cookies.
a Okay, let us imagine we can divide by zero, and see what happens. +
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