## 3.3.6 Arithmetic

### 3.3.6.1 Sets of numbers

 INT Integers NAT Natural numbers, starting with 0 NAT1 Natural numbers, starting with 1 .. Range of numbers
Description

The set of all integers is denoted by . It contains all elements of the type. The two subsets and contain all elements greater than or equal to 0 and 1 respectively. The range of numbers between and is denoted by .

Definition

Types

with and

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### 3.3.6.2 Arithmetic operations

 + Addition - Subtraction or unary minus * Multiplication / Integer division mod Modulo ^ Exponentiation
Description

These are the usual arithmetic operations.

Definition

Addition, subtraction and multiplication behave as expected.

The division is defined in a way that and :
for and

Types

With , for each operator of , , , , :

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### 3.3.6.3 Minimum and Maximum

 min Minimum max Maximum
Description

and denotes the smallest and largest number in the set of integers respectively.

The minimum and maximum are only defined if such a number exists.

Definition

Types

and with .

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