Number Sets and Mathematical Foundations

This page introduces the fundamental number sets in mathematics, establishing a hierarchical structure from basic to complex numbers. The content presents a visual representation of how different number sets relate to each other.

Definition: Number sets are collections of numbers with specific properties and characteristics.

Vocabulary:

• N (Natural Numbers): Positive whole numbers starting from 1
• Z (Integers): Includes all whole numbers, both positive and negative
• Q (Rational Numbers): Numbers that can be expressed as fractions
• R (Real Numbers): Encompasses all rational and irrational numbers

Example: Natural numbers include 1, 2, 3, 4..., while integers also include negative numbers like -2, -1, 0, 1, 2...

Highlight: The progression from N to R shows how number sets become increasingly comprehensive, with each set containing all previous sets.

Bracket Resolution

This final section explains methods for handling brackets in algebraic expressions, including multiplication and factoring.

Definition: Bracket resolution involves systematically removing or introducing brackets while maintaining the expression's value.

Example: When removing a negative sign before brackets, change all signs within: -(a + b - c) = -a - b + c

Highlight: Understanding bracket resolution is crucial for simplifying complex algebraic expressions and solving equations.