(part 2 of explaining)
There are mathematical structures in which {\textstyle {\tfrac {a}{0}}}{\textstyle {\tfrac {a}{0}}} is defined for some a such as in the Riemann sphere (a model of the extended complex plane) and the Projectively extended real line; however, such structures do not satisfy every ordinary rule of arithmetic (the field axioms).

In computing, a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, result in a special not-a-number value,[2] or crash.