error

In computing, a fault or mistake, either in the software or on the part of the user, that causes a program to stop running (crash) or produce unexpected results. Program errors, or bugs, are largely eliminated in the course of the programmer's initial testing procedure, but some will remain in most programs. All computer operating systems are designed to produce an error message (on the display screen, or in an error file or printout) whenever an error is detected, reporting that an error has taken place and, wherever possible, diagnosing its cause.

Errors can be categorized into several types:

syntax errors are caused by the incorrect use of the programming language, and include spelling and keying mistakes. These errors are detected when the compiler or interpreter fails to translate the program into machine code (instructions that a computer can understand directly); logical errors are faults in the program design – for example, in the order of instructions. They may cause a program to respond incorrectly to the user's requests or to crash completely; execution errors, or run-time errors, are caused by combinations of data that the programmer did not anticipate. A typical execution error is caused by attempting to divide a number by zero. This is impossible, and so the program stops running at this point. Execution errors occur only when a program is running, and cannot be detected by a compiler or interpreter.

Computers are designed to deal with a set range of numbers to a given range of accuracy. Many errors are caused by these limitations: overflow error occurs when a number is too large for the computer to deal with; an underflow error occurs when a number is too small; rounding and truncation errors are caused by the need to round off decimal numbers, or to cut them off (truncate them) after the maximum number of decimal places allowed by the computer's level of accuracy.

error

In mathematics, incorrect answer to a calculation. Also, the amount by which an incorrect answer differs from the correct one. This is usually denoted by δx for a figure whose correct value is x.

Errors in calculation may be the result of a mistake made while using a calculator, in which case they can be detected by means of a suitable checking procedure. Errors can also be generated by deliberate rounding used to simplify a calculation. Whenever a number is rounded it produces an error and this may be carried on through a calculation, compounding the error to an unacceptable level. To prevent this, rounding should usually be avoided until the final answer is reached.

The degree or level of accuracy of an answer is controlled by the number of significant figures or decimal places used in the rounding process and this will also give the error bounds for that answer. For example, an answer lying between 36.265 and 36.275 will be given as 36.27 to two decimal places. This can also be shown as 36.265 ≤ 36.27 < 36.275.