Number Systems in Mathematics

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, -2/3 (can be expressed as a finite decimal)
Irrational Numbers: non-repeating, non-terminating decimals, e.g. π, e
Real Numbers: union of rational and irrational numbers
Complex Numbers: numbers with real and imaginary parts, e.g. 3 + 4i

Equations: statements with equal signs, e.g. 2x + 3 = 5
Inequalities: statements with >, <, ≥, ≤, e.g. 2x - 3 > 2
Functions: relations between inputs (x) and outputs (y), e.g. f(x) = 2x^2 + 1
Graphs: visual representations of functions on a coordinate plane

Points: locations in space, represented by coordinates (x, y, z)
Lines: sets of points extending infinitely in two directions
Angles: measures of rotation between two lines or planes
Shapes: polygons (e.g. triangles, quadrilaterals), circles, and 3D objects (e.g. spheres, cubes)
Measurements: perimeter, area, volume, and surface area of shapes

Data: collections of information, often numerical
Probability: likelihood of events, measured between 0 and 1
Probability Distributions: patterns of probability, e.g. normal, binomial
Statistical Analysis: methods for interpreting and summarizing data, e.g. mean, median, mode, standard deviation

Natural numbers are positive integers (1, 2, 3,...) and are often used for counting.
Whole numbers include natural numbers and zero (0, 1, 2, 3,...) and represent non-negative integers.
Integers consist of both positive and negative whole numbers (...,-3, -2, -1, 0, 1, 2, 3,...) and are used to represent whole amounts.
Rational numbers are fractions (e.g. 3/4, -2/3) that can be expressed as finite decimals or ratios of integers.
Irrational numbers are non-repeating, non-terminating decimals (e.g. π, e) and cannot be expressed as simple fractions.
Real numbers are the combination of rational and irrational numbers and represent all possible decimal expansions.
Complex numbers have both real and imaginary parts (e.g. 3 + 4i) and are used to extend the real number system.

Equations are statements with equal signs (e.g. 2x + 3 = 5) used to express the equality of two mathematical expressions.
Inequalities are statements with greater than (>) or less than (<) signs (e.g. 2 > 1) used to compare values.
Functions are relations between input values (x) and output values (y) (e.g. f(x) = 2x^2 + 1) and are often represented graphically.
Graphs are visual representations of functions on a coordinate plane, allowing us to visualize relationships between variables.

Points are locations in space, represented by coordinates (x, y, z) and used to define geometric objects.
Lines are sets of points extending infinitely in two directions and can be used to define shapes and boundaries.
Angles are measures of rotation between two lines or planes and are essential in geometric calculations.
Shapes include two-dimensional polygons (e.g. triangles, quadrilaterals), circles, and three-dimensional objects (e.g. spheres, cubes).
Measurements in geometry involve calculating perimeter, area, volume, and surface area of shapes.

Limits are values that functions approach as input values change and are essential in understanding function behavior.
Derivatives measure rates of change of functions (e.g. velocity and acceleration) and are used to analyze function behavior.
Integrals are used to calculate the accumulation of rates of change (e.g. area under curves) and are essential in problems involving accumulation.

Data is a collection of information, often numerical, used to make inferences and conclusions.
Probability is a measure of the likelihood of events, ranging from 0 (impossible) to 1 (certain).
Probability distributions are patterns of probability, such as normal and binomial distributions, used to model real-world events.
Statistical analysis involves methods for interpreting and summarizing data, including calculating mean, median, mode, and standard deviation.