Number Systems Basics

Numbers and Operations

• Number Systems:

  • Natural Numbers (1, 2, 3, ...): positive integers
  • Whole Numbers (0, 1, 2, 3, ...): non-negative integers
  • Integers (...,-3, -2, -1, 0, 1, 2, 3, ...): positive and negative whole numbers
  • Rational Numbers (fractions, decimals, percentages): can be expressed as a/b, where a and b are integers and b ≠ 0
  • Irrational Numbers (π, e, √2, ...): cannot be expressed as a simple fraction
  • Real Numbers: includes rational and irrational numbers
  • Complex Numbers: includes real and imaginary numbers (a + bi, where a and b are real numbers and i is the imaginary unit)

• Basic Operations:

  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)
  • Exponents (^)
  • Roots (√)

Algebra

• Equations and Inequalities:

  • Linear Equations (ax + by = c): degree 1, graph is a straight line
  • Quadratic Equations (ax^2 + bx + c = 0): degree 2, graph is a parabola
  • Systems of Equations: multiple equations with multiple variables
  • Inequalities: statements with <, >, ≤, ≥, or ≠

• Functions:

  • Domain: set of input values
  • Range: set of output values
  • Composition: combining functions
  • Inverse: reversing the input and output

Geometry

• Points, Lines, and Planes:

  • Points: locations in space, represented by coordinates (x, y, z)
  • Lines: sets of points, can be extended infinitely
  • Planes: flat surfaces, can be extended infinitely

• Angles and Measurement:

  • Angle: formed by two rays sharing a common endpoint
  • Types of Angles: acute, right, obtuse, straight, reflex
  • Measurement: degrees, radians, minutes, seconds

Data Analysis and Statistics

• Data Types:

  • Quantitative: numerical data (e.g., height, weight)
  • Qualitative: categorical data (e.g., gender, color)

• Graphs and Charts:

  • Types: bar, histogram, box plot, scatter plot, pie chart
  • Purpose: visualize and understand data distributions

• Descriptive Statistics:

  • Measures of Central Tendency: mean, median, mode
  • Measures of Variation: range, variance, standard deviation

Numbers and Operations

• Natural Numbers are positive integers (1, 2, 3,...)
• Whole Numbers are non-negative integers (0, 1, 2, 3,...)
• Integers include positive and negative whole numbers (...,-3, -2, -1, 0, 1, 2, 3,...)
• Rational Numbers can be expressed as a/b, where a and b are integers and b ≠ 0 (fractions, decimals, percentages)
• Irrational Numbers cannot be expressed as a simple fraction (π, e, √2,...)
• Real Numbers include rational and irrational numbers
• Complex Numbers include real and imaginary numbers (a + bi, where a and b are real numbers and i is the imaginary unit)
• Basic Operations include Addition (+), Subtraction (-), Multiplication (×), Division (÷), Exponents (^), and Roots (√)

Algebra

• Linear Equations are degree 1 and graph as a straight line (ax + by = c)
• Quadratic Equations are degree 2 and graph as a parabola (ax^2 + bx + c = 0)
• Systems of Equations involve multiple equations with multiple variables
• Inequalities are statements with , ≤, ≥, or ≠
• Domain is the set of input values for a function
• Range is the set of output values for a function
• Composition involves combining functions
• Inverse involves reversing the input and output of a function

Geometry

• Points are locations in space, represented by coordinates (x, y, z)
• Lines are sets of points and can be extended infinitely
• Planes are flat surfaces that can be extended infinitely
• Angles are formed by two rays sharing a common endpoint
• Angle types include acute, right, obtuse, straight, and reflex
• Measurement units include degrees, radians, minutes, and seconds

Data Analysis and Statistics

• Quantitative Data is numerical (e.g., height, weight)
• Qualitative Data is categorical (e.g., gender, color)
• Graph types include bar, histogram, box plot, scatter plot, and pie chart
• Graphs are used to visualize and understand data distributions
• Measures of Central Tendency include mean, median, and mode
• Measures of Variation include range, variance, and standard deviation

Explore the fundamentals of number systems, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. Learn the definitions and characteristics of each type.