Documentation

<>, _unequal

Inequalities (unequal)

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x <> y
_unequal(x, y)

Description

x <> y defines an inequality.

x <> y is equivalent to the function call _unequal(x, y).

The operator <> returns a symbolic expression representing an inequality.

The resulting expression can be evaluated to TRUE or FALSE by the function bool. It also serves as control conditions in if, repeat, and while statements. In all these cases, testing for equality or inequality is a purely syntactical test. For example, bool(0.5 <> 1/2) returns TRUE although both numbers coincide numerically. Further, Boolean expressions can be evaluated to TRUE, FALSE, or UNKNOWN by the function is. Tests using is semantically compare x and y applying mathematical considerations.

Inequalities have two operands: the left side and the right side. Use lhs and rhs to extract these operands.

The boolean expression not x = y is always converted to x <> y.

The expression not x <> y is always converted to x = y.

Examples

Example 1

In the following example, note the difference between syntactical and numerical equality. The numbers 1.5 and coincide numerically. However, 1.5 is of domain type DOM_FLOAT, whereas is of domain type DOM_RAT. Consequently, they are not regarded as equal in the following syntactical test:

1.5 <> 3/2;
bool(%)  The following expressions coincide syntactically:

_unequal(1/x, diff(ln(x),x));
bool(%)  The Boolean operator not converts equalities and inequalities:

not a = b, not a <> b Example 2

In this example, use the operator <> to compare two tables:

bool(table(a = PI) <> table(a = sqrt(2))) Example 3

Test equality of these expressions by using the syntactical test via bool and the semantical test via testeq:

bool(1 <> x/(x + y) + y/(x + y)),
testeq(1 <> x/(x + y) + y/(x + y)) Example 4

Inequalities are typical input objects for system functions, such as solve:

solve(x^2 - 2*x <> -1, x) Parameters

 x, y Arbitrary MuPAD® objects

Return Values

Expression of type "_unequal".