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The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math.
| Symbol | Name | Read as | Meaning | Example(s) |
|---|---|---|---|---|
= | Equal | is equal to | If x=y, x and y represent the same value or thing. | 5(2)=10 |
≡ | Definition | is defined as | If x≡y, x is defined as another name of y | ϕ≡(√5+1)/2≈1.618 |
≈ | Approximately equal | is approximately equal to | If x≈y, x and y are almost equal. | √2≈1.41 |
≠ | Inequation | does not equal, is not equal to | If x≠y, x and y do not represent the same value or thing. | 1+1≠3 |
< | Strict inequality | is less than | If x<y, x is less than y. | 4<5 |
> | is greater than | If x>y, x is greater than y. | 3>2 | |
≪ | is much less than | If x≪y, x is much less than y. | 0.001≪999999999 | |
≫ | is much greater than | If x≫y, x is much greater than y. | 999999999≫0.001 | |
≤ | Inequality | is less than or equal to | If x≤y, x is less than or equal to y. | 5≤6 and 5≤5 |
≥ | is greater than or equal to | If x≥y, x is greater than or equal to y. | 2≥1 and 2≥2 | |
∝ | Proportionality | is proportional to | If x∝y, then y=kx for some constant k. | If y=4x then y∝x and x∝y |
+ | Addition | plus | x+y is the sum of x and y. | 2+3=5 |
- | Subtraction | minus | x-y is the subtraction of y from x | 5-3=2 |
× or · | Multiplication | times or multiplied by | x×y or x·y is the multiplication of x by y | 4×5=20 or 4·5=20 |
÷ or / | Division | divided by | x÷y or x/y is the division of x by y | 20÷4=5 or 20/4=5 |
± | Plus-minus | plus or minus | x±y means both x+y and x-y | 1±2 represents both 3 and -1 |
∓ | Minus-plus | minus or plus | 4±(3∓5) means both 4+(3-5) and 4-(3+5) | 6∓(1±3)=2 or 4 |
√ | Square root | square root | √x is a nonnegative number whose square is x. | √4=2 |
∑ | Summation | sum over … from … to … of, sigma | \displaystyle{ \sum_{k=1}^{n}{x_k} } is the same as x1+x2+x3+...+xn | \displaystyle{ \sum_{k=1}^{5}{(k+2)}=3+4+5+6+7=25 } |
∏ | Product | product over … from … to … of | \displaystyle{ \prod_{k=1}^{n}{x_k} } is the same as x1×x2×x3×....×xn | \displaystyle{ \prod_{k=1}^{5}{k} }=1×2×3×4×5=120 |
! | Factorial | factorial | n! is the product 1×2×3...×n | 5!=1×2×3×4×5=120 |
⇒ | Material implication | implies | A⇒B means that if A is true, B must also be true, but if A is false, B is unknown. | x=3⇒x2=9, but x2=9⇒x=3 is false, because x could also be -3. |
⇔ | Material equivalence | if and only if | If A is true, B is true and if A is false, B is false. | x=y+1⇔x-1=y |
|…| | Absolute value | absolute value of | |x| is the distance along the real line (or across the complex plane) between x and zero. | |x|=x and |-x|=x |
|| | Parallel | is parallel to | If A||B then line A will never touch line B, thus both lines are rotated in the same angle. | x||(x+1) |
⊥ | Perpendicular | is perpendicular to | If A⊥B then line A is touching line B in a 90 degrees angle. | x⊥y |
≅ | Congruence | is congruent to | If A≅B then shape A and B same shape and size, or A has the same shape and size as the mirror image of B. | If two triangles, △ABC and △DEF, are congruent, it can be denoted as △ABC≅△DEF |
φ | Golden ratio | golden ratio | The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887. | φ ≈ 1.6180339887 |
∞ | Infinity | infinity | ∞ is a symbol used to represent unending amounts. | ∞ + x = ∞ |
∈ | Set membership | is an element of | a∈S means that a is an element of the set S | 3.5∈ℝ, 1∈ℕ, 1+i∈ℂ |
∉ | is not an element of | a∉S means that a is not an element of the set S | 2.1∉ℕ, 1+i∉ℝ | |
{,} | Set brackets | the set of | {a,b,c} is the set consisting of a, b, and c | S = { a, b, c } |
ℕ | Natural numbers | N | ℕ denotes the set of natural numbers | 1∈ℕ, 2∈ℕ, 100∈ℕ |
ℤ | Integers | Z | ℤ denotes the set of integers | -1∈ℤ, 0∈ℤ, 30∈ℤ |
ℚ | Rational numbers | Q | ℚ denotes the set of rational numbers | 8.323∈ℚ, 7∈ℚ, π∉ℚ |
ℝ | Real numbers | R | ℝ denotes the set of real numbers | π∈ℝ, 7∈ℝ, √(-1)∉ℝ |
ℂ | Complex numbers | C | ℂ denotes the set of complex numbers | √(-1)∈ℂ |
x̄ | Mean | bar, overbar | x̄ is the mean (average) of xi | if x={1,2,3} then x̄=2 |
x̄ | Complex conjugate | the complex conjugate of x | If x=a ± bi, then x̄=a ∓ bi where i=√(-1) | x=-4 + 5.3i, x̄=-4 - 5.3i |
| [+|-] | Situational plus minus | Either plus or minus depending on the situation. | If y=[+|-]x then x is either positive or negative depending on the situation. | y=[+|-]x y equals either +x or -x depending on the scenario. |