Mathematical Symbols and Their Meanings

Study Notes

Mathematical Symbols and Their Meanings

Equality: = (equals sign) Indicates equality of two values. Example: 5 = 2 + 3
Inequality: ≠ (not equal sign) Indicates that two values are not equal. Example: 5 ≠ 6
Approximately Equal: ≈ (approximately equal) Indicates that two values are approximately equal. Example: sin(0.01) ≈ 0.01
Strict Inequality: > (greater than) Indicates that a value is strictly greater than another. Example: 5 > 4
Strict Inequality: < (less than) Indicates that a value is strictly less than another. Example: 5 < 6
Inequality: ≥ (greater than or equal to) Indicates that a value is greater than or equal to another. Example: x ≥ y
Inequality: ≤ (less than or equal to) Indicates that a value is less than or equal to another. Example: x ≤ y
Parentheses: () Used to group expressions or indicate operations. Calculate the expression in parentheses first. Example: 2 * (3 + 5) = 16
Brackets: [] Similar to parentheses, used for grouping. Calculate the expression in brackets first. Example: [(1 + 2) * (1 + 5)] = 18
Plus: + (plus sign) Used for addition. Example: 1 + 1 = 2
Minus: - (minus sign) Used for subtraction. Example: 2 - 1 = 1
Plus-Minus: ± Used to indicate both positive and negative values. Example: 3 ± 5 = 8 or 2
Minus-Plus: ∓ Used to indicate a specific choice or relationship when both plus and minus values might arise. Example: 3 ∓ 5 = 2 or 8.
Times: × (times sign) Used for multiplication. Example: 2 × 3 = 6
Multiplication Dot: ⋅ Used for multiplication. Example: 2 ⋅ 3 = 6
Division: / or ÷ (division sign) Used for division. Example: 6 ÷ 3 = 2 or 6/3 = 2
Horizontal Line: Used for division/ fractions. Example: 6/3 = 2
Decimal Point/Separator: . (period) Used to separate the whole number part from the decimal part. Example: 2.56
Power/ Exponent: ab (superscript) Example: 2³ = 8
Square Root: √ Example: √9 = 3
Cube Root: ∛ Example: ∛8 = 2
Fourth Root: 4√ Example: ⁴√16 = 2
n-th Root: n√ (n in subscript) Example: ³√8 = 2
Absolute Value (Modulus): | | Example: |5| = 5
Percent: % Example: 10% × 30 = 3
Equivalence: ≡ Example A ≡ B Identical
Proportional to: ∝ Indicates a proportionality relationship Example: y ∝ x when y = kx, k constant
Much greater than: >> Example: a >> b Much greater than
Factorial: ! Example: 4! = 1 × 2 × 3 × 4 = 24
Open Interval: (a, b) set of values between a and b, not inclusive of a and b. Example (2, 6)
Closed Interval: [a, b] set of values between a and b, inclusive of a and b. Example [2, 6]
Change/Difference: Δ Example: Δt = t₁ - t₀
Discriminant: Δ Example: Δ = b² - 4ac
Summation: Σ (sigma) Example: Σ (a_i) for i in a range of values.
Set: {} (Curly braces) Example sets: A = {3, 7, 9, 14}
Intersection: ∩ (Intersection symbol) Example: A ∩ B
Union: ∪ (Union symbol) Example: A ∪ B
Subset: ⊂ (Subset symbol) Example A ⊂ B (A is a subset of B)
Strict/Proper Subset: ⊂ or ⊆ A is a subset of B but not equal to B.
Implies: → Example: A → B (A implies B)
Equivalent to: ⇔ Example: A ⇔ B (A equivalent to B)
For all: ∀
There exists: ∃
Derivative: dy/dx or y'
Partial Derivative: ∂f(x, y)/∂x
Integral: ∫

Additional Note:

Many symbols have multiple meanings, depending on the context of the formula or equation.

Description

This quiz explores various mathematical symbols and their meanings. You'll learn how to interpret signs such as equality, inequality, and grouping symbols. Test your understanding of these key concepts that are fundamental in mathematics.