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However, more insidious are missing solutions, which can occur when performing operations on expressions that are invalid for certain values of those expressions. For example, if we were solving the following equation, the correct solution is obtained by subtracting 4 {\displaystyle 4} from both sides, then dividing both sides by 2 ...
ColdFusion: the built-in PrecisionEvaluate() function evaluates one or more string expressions, dynamically, from left to right, using BigDecimal precision arithmetic to calculate the values of arbitrary precision arithmetic expressions. D: standard library module std.bigint; Dart: the built-in int datatype implements arbitrary-precision ...
For a function to have an inverse, it must be one-to-one.If a function is not one-to-one, it may be possible to define a partial inverse of by restricting the domain. For example, the function = defined on the whole of is not one-to-one since = for any .
For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the value of the expression may be undefined. Thus an expression represents an operation over constants and free variables and whose output is the resulting value of the expression. [22]
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
Dimensional analysis may be used as a sanity check of physical equations: the two sides of any equation must be commensurable or have the same dimensions. A person who has calculated the power output of a car to be 700 kJ may have omitted a factor, since the unit joules is a measure of energy, not power (energy per unit time).
In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system. [1]Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system.
Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced to the computation of square and cube roots.