# <>, _unequal

Inequalities (unequal)

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

````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"`.