math operation

Type

glossary

Description

Any of the math operations in command, function or infix form, including arithmetic, exponential, logarithmic, trigonometric and statistical functions.

A math operation can cause one of three different execution errors to be thrown:

• "numeric: domain error"
• "numeric: range error (overflow)"
• "numeric: divide by zero"

A domain error occurs when a math operation, given finite inputs, results in not-a-number (NaN) - this is the case when the function is not defined for the given inputs, for example acos(2); or the output does not exist in the extended real line (ℝ ∪ {−∞, +∞}), for example, sqrt(-1).

A range error occurs when a math operation's output overflows given finite inputs, i.e. when the result is greater than the maximum value of a 64-bit floating point, for example 10^308 * 2.

A divide by zero error occurs when a math operation causes division by zero either directly, for example 1/0 or 0^-1 or as part of its computation, for example 10 wrap 0.

Math operations do not throw execution errors when any of the inputs are non-finite, for example neither of (1^(-inf) + inf) / 2 = inf or sqrt(-inf) = NaN causes an execution error.