Number Systems and Algebra Basics

Number Systems

• Natural Numbers: Positive integers, e.g. 1, 2, 3, ...
• Whole Numbers: Non-negative integers, e.g. 0, 1, 2, 3, ...
• Integers: Positive and negative whole numbers, e.g. ..., -3, -2, -1, 0, 1, 2, 3, ...
• Rational Numbers: Fractions, e.g. 3/4, 22/7, ...
• Irrational Numbers: Non-repeating decimals, e.g. π, e, ...
• Real Numbers: Rational and irrational numbers, e.g. ..., -3, -2, -1, 0, 1, 2, 3, ..., π, e, ...

Algebra

• Variables: Letters or symbols representing unknown values, e.g. x, y, z
• Constants: Numbers, e.g. 2, 5, 10
• Expressions: Combinations of variables and constants, e.g. 2x + 5, x^2 - 3
• Equations: Statements of equality, e.g. 2x + 5 = 11, x^2 - 3 = 7
• Inequalities: Statements of inequality, e.g. 2x + 5 > 11, x^2 - 3 ≤ 7

Geometry

• Points: Locations in space, e.g. (x, y), (3, 4)
• Lines: Sets of points extending infinitely, e.g. x = 2, y = 3x - 1
• Angles: Measures of rotation, e.g. 30°, 90°, 180°
• Triangles: Polygons with three sides, e.g. equilateral, isosceles, scalene
• Circles: Sets of points equidistant from a central point, e.g. (x - 2)^2 + (y - 3)^2 = 4

Calculus

• Limits: Approaching values, e.g. lim (x → 2) (x^2) = 4
• Derivatives: Rates of change, e.g. d/dx (x^2) = 2x
• Integrals: Accumulations, e.g. ∫(x^2) dx = (1/3)x^3 + C

Statistics

• Mean: Average value, e.g. (2 + 4 + 6) / 3 = 4
• Median: Middle value, e.g. 2, 4, 6, ... (middle value)
• Mode: Most frequent value, e.g. 2, 2, 4, 6, ... (most frequent value)
• Standard Deviation: Measure of variation, e.g. σ = √[(Σ(x - μ)^2) / (n - 1)]

Number Systems

• Natural numbers are positive integers, such as 1, 2, and 3.
• Whole numbers are non-negative integers, including 0, 1, 2, and 3.
• Integers include both positive and negative whole numbers, such as ..., -3, -2, -1, 0, 1, 2, and 3.
• Rational numbers are fractions, like 3/4 and 22/7.
• Irrational numbers have non-repeating decimals, such as π and e.
• Real numbers encompass both rational and irrational numbers.

Algebra

• Variables are letters or symbols representing unknown values, like x, y, and z.
• Constants are numbers, such as 2, 5, and 10.
• Expressions combine variables and constants, like 2x + 5 and x^2 - 3.
• Equations are statements of equality, such as 2x + 5 = 11 and x^2 - 3 = 7.
• Inequalities are statements of inequality, like 2x + 5 > 11 and x^2 - 3 ≤ 7.

Geometry

• Points are locations in space, represented by coordinates like (x, y) or (3, 4).
• Lines are sets of points extending infinitely, such as x = 2 and y = 3x - 1.
• Angles are measures of rotation, like 30°, 90°, and 180°.
• Triangles are polygons with three sides, including equilateral, isosceles, and scalene triangles.
• Circles are sets of points equidistant from a central point, like (x - 2)^2 + (y - 3)^2 = 4.

Calculus

• Limits approach specific values, such as lim (x → 2) (x^2) = 4.
• Derivatives measure rates of change, like d/dx (x^2) = 2x.
• Integrals represent accumulations, like ∫(x^2) dx = (1/3)x^3 + C.

Statistics

• The mean is the average value, calculated by summing values and dividing by the number of values, like (2 + 4 + 6) / 3 = 4.
• The median is the middle value when values are arranged in order, like 2, 4, 6,... (middle value).
• The mode is the most frequent value, like 2, 2, 4, 6,... (most frequent value).
• Standard deviation measures variation, calculated as σ = √[(Σ(x - μ)^2) / (n - 1)].