What is the reciprocal of 0?
0 does not have a reciprocal. By definition, the reciprocal of x is a number y such that xy = 1. There is no number that you can multiply by 0 and get 1.
Contrary to the belief of many responses, the reciprocal of 0 is NOT infinity. Infinity is not a real number, so it can't be the reciprocal of anything if we are working in the real numbers. Also, it is not true that zero times infinity is one. In fact, in some cases, zero times infinity is defined to be zero.
There is a correct concept in their misstatement, however. When taking a limit of a function of the form f(x)/g(x), if f(x) -> 1 and g(x) -> 0 as x -> c (c may be finite or +/-infinity), then the quotient f(x)/g(x) will become infinitely large in size. But, that does NOT mean that we can say 1/0 = infinity.
0 does not have a reciprocal. By definition, the reciprocal of x is a number y such that xy = 1. There is no number that you can multiply by 0 and get 1.
Contrary to the belief of many responses, the reciprocal of 0 is NOT infinity. Infinity is not a real number, so it can't be the reciprocal of anything if we are working in the real numbers. Also, it is not true that zero times infinity is one. In fact, in some cases, zero times infinity is defined to be zero.
There is a correct concept in their misstatement, however. When taking a limit of a function of the form f(x)/g(x), if f(x) -> 1 and g(x) -> 0 as x -> c (c may be finite or +/-infinity), then the quotient f(x)/g(x) will become infinitely large in size. But, that does NOT mean that we can say 1/0 = infinity.
