Documentation

# `Type`::`Real`

Type and property representing real numbers

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## Syntax

```testtype(`obj`, Type::Real)
assume(`x`, Type::Real)
is(`ex`, Type::Real)
```

## Description

`Type::Real` represents real numbers. `Type::Real` is a property, too, which can be used in an `assume` call.

The call `testtype(obj, Type::Real)` checks, whether `obj` is a real number and, if it is, returns `TRUE`, otherwise `FALSE`.

`testtype` only performs a syntactical test identifying MuPAD® objects of type `DOM_INT`, `DOM_RAT` and `DOM_FLOAT`. This does not include arithmetical expressions such as `exp(1)`, which are not identified as of type `Type::Real`.

The call `assume(x, Type::Real)` marks the identifier `x` as a real number.

The call `is(ex, Type::Real)` derives, whether the expression `ex` is a real number (or this property can be derived).

This type represents a property that can be used in `assume` and `is`.

## Examples

### Example 1

The following numbers are of type `Type::Real`:

```testtype(2, Type::Real), testtype(3/4, Type::Real), testtype(0.123, Type::Real), testtype(-1, Type::Real), testtype(-1.02, Type::Real)```

The following expressions are exact representations of real numbers, but syntactically they are not of `Type::Real`:

```testtype(exp(1), Type::Real), testtype(PI^2 + 5, Type::Real), testtype(sin(2), Type::Real)```

The function `is` performs a semantical, mathematically more useful check:

```is(exp(1), Type::Real), is(PI^2 + 5, Type::Real), is(sin(2), Type::Real)```

### Example 2

Integers are real numbers:

```assume(x, Type::Integer): is(x, Type::Real)```

But real numbers can be integer or not:

```assume(x, Type::Real): is(x, Type::Integer)```

The sine of a real number is a real number in the interval [- 1, 1]:

`getprop(sin(x))`

`delete x:`

## Parameters

 `obj` Any MuPAD object `x` An identifier or a mathematical expression containing identifiers `ex`