A0

A0, A-0, A₀, or a₀ may refer to:

Airplanes and rockets

A-0 System

The A-0 system (Arithmetic Language version 0), written by Grace Hopper in 1951 and 1952 for the UNIVAC I, was the first compiler ever developed for an electronic computer. The A-0 functioned more as a loader or linker than the modern notion of a compiler. A program was specified as a sequence of subroutines and arguments. The subroutines were identified by a numeric code and the arguments to the subroutines were written directly after each subroutine code. The A-0 system converted the specification into machine code that could be fed into the computer a second time to execute the said program.

The A-0 system was followed by the A-1, A-2, A-3 (released as ARITH-MATIC), AT-3 (released as MATH-MATIC) and B-0 (released as FLOW-MATIC).

The A-2 system was developed at the UNIVAC division of Remington Rand in 1953 and released to customers by the end of that year. Customers were provided the source code for A-2 and invited to send their improvements back to UNIVAC. Thus A-2 was an early, and perhaps the first, example of free and open-source software.

Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in George Berkeley's criticism of infinitesimal calculus in The Analyst ("ghosts of departed quantities").

There are mathematical structures in which a/0 is defined for some a such as in the Riemann sphere and the real projective line; however, such structures cannot 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, freezes via infinite loop, or a crash.