Integer Numbers and Operations

This section focuses on relative numbers (integers) and their operations, expanding beyond natural numbers to include negative values.

Definition: The set of integer numbers (Z) includes positive numbers $Z+$, negative numbers $Z-$, and zero.

Vocabulary:

• Opposite numbers: Numbers with different signs but the same absolute value
• Concordant numbers: Numbers with the same sign
• Discordant numbers: Numbers with different signs

Example: +8 and +6 are concordant, while -7 and +12 are discordant. -9 and +9 are both discordant and opposite.

Highlight: The sum of two integers follows specific rules based on whether the numbers are concordant or discordant:

• For concordant numbers: The result maintains their common sign
• For discordant numbers: The result takes the sign of the number with the larger absolute value

Natural Numbers and Basic Operations

This section introduces the fundamental concepts of numeri naturali and basic mathematical operations. Natural numbers are defined as the set of counting numbers starting from 0, represented as N = {0, 1, 2, 3, 4, 5, 6, 7...}.

Definition: Natural numbers are whole, infinite, and positive numbers that can be represented on an oriented half-line showing their ordered nature.

Highlight: The four basic operations possible with natural numbers are addition, subtraction, multiplication, and division.

Example: Powers are represented as repeated multiplications, such as 3³ = 81, where 3 is the base and 3 is the exponent.

The page also covers the properties of operations, including:

Vocabulary:

• Zero as the neutral element of addition
• One as the neutral element of multiplication
• Zero as the absorbing element of multiplication

The section concludes with an introduction to mcm e m.c.d., defining them as essential concepts for working with natural numbers.