Types of Numbers in Mathematics

Numbers

• Natural Numbers: 1, 2, 3, ... (positive integers)
• Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (all whole numbers and their opposites)
• Rational Numbers: fractions, decimals, and percentages (can be expressed as a ratio of integers)
• Irrational Numbers: cannot be expressed as a ratio of integers (e.g. π, e, √2)
• Real Numbers: all rational and irrational numbers
• Complex Numbers: numbers with real and imaginary parts (e.g. 3 + 4i)

Operations

• Addition: combining two or more numbers to get a total or a sum
• Subtraction: finding the difference between two numbers
• Multiplication: repeated addition, or the product of two or more numbers
• Division: sharing a quantity into equal parts, or finding how many times one number fits into another
• Exponents: powers of numbers (e.g. 2^3 means 2 to the power of 3)
• Roots: the opposite of exponents (e.g. √4 means the square root of 4)

Algebra

• Variables: letters or symbols representing unknown values
• Constants: numbers that do not change value
• Expressions: combinations of variables, constants, and operations
• Equations: statements saying that two expressions are equal
• Inequalities: statements saying that one expression is greater than, less than, or equal to another

Geometry

• Points: locations in space, represented by coordinates
• Lines: sets of points extending infinitely in two directions
• Rays: sets of points extending infinitely in one direction
• Angles: formed by two rays sharing a common endpoint
• Triangles: shapes with three sides and three angles
• Circles: sets of points equidistant from a central point

Measurement

• Length: distance between two points
• Area: amount of space inside a shape
• Volume: amount of space inside a 3D object
• Capacity: amount of liquid a container can hold
• Mass: amount of matter in an object
• Time: duration between events

Data Analysis

• Types of Data: qualitative (descriptive), quantitative (numerical), and categorical (grouped)
• Graphs: visual representations of data (e.g. bar graphs, pie charts, line graphs)
• Statistics: methods for collecting, analyzing, and interpreting data
• Probability: chance or likelihood of an event occurring

Numbers

• Natural Numbers: Positive integers starting from 1 (1, 2, 3,...).
• Whole Numbers: All non-negative integers including zero (0, 1, 2, 3,...).
• Integers: Includes all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3,...).
• Rational Numbers: Can be expressed as a fraction or ratio of integers, includes terminating and repeating decimals.
• Irrational Numbers: Cannot be expressed as a fraction, examples include π, e, and √2.
• Real Numbers: Comprise both rational and irrational numbers, covering all number lines.
• Complex Numbers: Formed by a real part and an imaginary part, represented as (a + bi), where i is the imaginary unit.

Operations

• Addition: The process of combining numbers to find a total.
• Subtraction: The operation of determining the difference between two numbers.
• Multiplication: Expresses repeated addition of a number or numbers.
• Division: Involves splitting a quantity into equal parts or determining how many times one number fits into another.
• Exponents: Notation that indicates the power to which a number is raised (e.g., 2^3 means 2 multiplied by itself three times).
• Roots: Operation finding a value that, when raised to a certain power, gives the original number (e.g., √4 returns 2).

Algebra

• Variables: Symbols such as x or y used to represent unknown values in expressions and equations.
• Constants: Fixed values that do not change throughout a problem or equation.
• Expressions: Combinations of variables, constants, and operations that represent a mathematical quantity.
• Equations: Mathematical statements indicating that two expressions are equivalent.
• Inequalities: Comparisons between two expressions showing their relative sizes (greater than, less than, or equal).

Geometry

• Points: Defined locations in space marked by coordinates with no size or dimension.
• Lines: Straight paths extending infinitely in both directions, containing infinite points.
• Rays: Similar to lines but extend infinitely in one direction from a starting point.
• Angles: Formed by the intersection of two rays at a common endpoint, measured in degrees.
• Triangles: Polygons with three sides and three angles, classified by angles and side lengths.
• Circles: Closed curves where all points are equidistant from a fixed central point.

Measurement

• Length: The straight-line distance between two points, usually measured in units such as meters or inches.
• Area: The total space contained within a shape, measured in square units.
• Volume: The three-dimensional space an object occupies, measured in cubic units.
• Capacity: Refers to the amount of liquid a container can hold, commonly measured in liters or gallons.
• Mass: A measurement of the amount of matter present in an object, often measured in grams or kilograms.
• Time: The duration between two events, quantifiable in units like seconds, minutes, or hours.

Data Analysis

• Types of Data: Includes qualitative (descriptive attributes), quantitative (numerical measurements), and categorical (grouped classifications).
• Graphs: Graphical means to represent data visually, includes bar graphs, pie charts, and line graphs for easy interpretation.
• Statistics: Techniques for collecting, analyzing, and interpreting data to infer conclusions.
• Probability: Measures the chance of an event occurring, often expressed as a fraction or percentage.