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.