Number Systems in Mathematics

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, e.g. 3/4, 22/7 (can be expressed as a finite decimal)
• Irrational Numbers: non-repeating, non-terminating decimals, e.g. π, e
• Real Numbers: includes all rational and irrational numbers
• Complex Numbers: numbers with real and imaginary parts, e.g. 3 + 4i

Algebra

• Variables: letters or symbols that represent unknown values
• Constants: numbers that do not change value
• Expressions: combinations of variables, constants, and operations
• Equations: statements that express the equality of two expressions
• Inequalities: statements that compare two expressions using >, <, ≥, or ≤

Geometry

• Points: locations in space, represented by coordinates (x, y)
• Lines: sets of points that extend infinitely in two directions
• Rays: lines that extend from a point to infinity in one direction
• Angles: formed by two rays sharing a common endpoint
• Triangles: three-sided polygons with three angles and three sides
• Quadrilaterals: four-sided polygons with four angles and four sides

Calculus

• Limits: the behavior of a function as the input approaches a certain value
• Derivatives: measures of how functions change as the input changes
• Integrals: measures of the accumulation of a function over a given interval
• Differentiation: finding the derivative of a function
• Integration: finding the integral of a function

Statistics

• Descriptive Statistics: summarizing and describing data
  • Mean: average value of a dataset
  • Median: middle value of a dataset when arranged in order
  • Mode: most frequently occurring value in a dataset
  • Range: difference between the largest and smallest values in a dataset
• Inferential Statistics: making conclusions about a population based on a sample
  • Hypothesis Testing: testing a hypothesis about a population using a sample
  • Confidence Intervals: estimating a population parameter using a sample

Number Systems

• Natural numbers are a set of positive integers, starting from 1 and going up to infinity.
• Whole numbers include all natural numbers, plus the number 0.
• Integers are a set of whole numbers, including both positive and negative numbers.
• Rational numbers are fractions that can be expressed as a finite decimal, such as 3/4 or 22/7.
• Irrational numbers are non-repeating, non-terminating decimals, such as π (pi) or e.
• Real numbers are a combination of both rational and irrational numbers.

Algebra

• Variables are letters or symbols used to represent unknown values in algebraic expressions.
• Constants are numbers that do not change value, such as 2 or 5.
• Algebraic expressions combine variables, constants, and operations to form a mathematical statement.
• Equations are statements that express the equality of two algebraic expressions, often using the equal sign (=).
• Inequalities are statements that compare two algebraic expressions using greater than (>), less than (<), or other comparison operators.

Learn about the different types of number systems, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. Understand the definitions and relationships between these number systems.