# Math Notation Flashcards

≠

not equal sign

Inequality

5 ≠ 4

5 is not equal to 4

=

equals sign

Equality

5 = 2+3

5 is equal to 2+3

≈

approximately equal

approximation

x ≈ y means x is approximately equal to y

>

inequality

greater than

5 > 4

5 is greater than 4

inequality

less than

4 < 5

4 is less than 5

≥

inequality

greater than or equal to

5 ≥ 4,

x ≥ y means x is greater than or equal to y

≤

less than or equal to

4 ≤ 5,

x ≤ y means x is less than or equal to y

( )

parentheses

calculate expression inside first

2 × (3+5) = 16

[ ]

Brackets

calculate expression inside first

[(1+2)×(1+5)] = 18

+

plus sign

Addition

1 + 1 = 2

−

minus sign

Subtraction

2 − 1 = 1

±

plus - minus

both plus and minus operations

3 ± 5 = 8 or -2

*

Asterisk

Multiplication

2 * 3 = 6

×

times sign

Multiplication

2 × 3 = 6

⋅

multiplication dot

Multiplication

2 ⋅ 3 = 6

÷

division sign / obelus

Division

6 ÷ 2 = 3

/

division slash

Division

6 / 2 = 3

—

horizontal line

division / fraction

mod

Modulo

remainder calculation

7 mod 2 = 1

.

Period

decimal point, decimal separator

2.56 = 2+56/100

a^b

Caret

Exponent

2 ^ 3 = 8

√a

square root

√a ⋅ √a = a

√9 = ±3

3√a (3 superindex)

cube root

3√a ⋅ 3√a ⋅ 3√a = a

3√8 = 2

n√a (n superindex)

“n-th root (radical)

for n=3, n√8 = 2”

%

Percent

1% = 1/100

10% × 30 = 3

‰

Per-mille

1‰ = 1/1000 = 0.1%

10‰ × 30 = 0.3

ppm

Per-million

1ppm = 1/1000000

10ppm × 30 = 0.0003

ppb

Per-billion

1ppb = 1/1000000000

10ppb × 30 = 3×10-7

∠

Angle

formed by two rays

∠ABC = 30°

°

Degree

1 turn = 360°

α = 60°

deg

Degree

1 turn = 360deg

α = 60deg

≅

congruent to

equivalence of geometric shapes and size

∆ABC≅ ∆XYZ

~ (geometry)

Similarity

same shapes, not same size

∆ABC~ ∆XYZ

Δ

Triangle

triangle shape

ΔABC≅ ΔBCD

|x-y|

Distance

distance between points x and y

x-y | = 5

π

pi constant

π = 3.141592654…

c = π⋅d = 2⋅π⋅r

rad

Radians

radians angle unit

360° = 2π rad

c

Radians

radians angle unit

360° = 2π c

x

x variable

unknown value to find

when 2x = 4, then x = 2

≡

Equivalence

identical to

≜

equal by definition

:=

equal by definition

~

approximately equal

weak approximation

11 ~ 10

≈

approximately equal

Approximation

sin(0.01) ≈ 0.01

∝

proportional to

y ∝ x when y = kx, k constant

∞

Lemniscate

infinity symbol

≪

much less than

1 ≪ 1000000

≫

much greater than

1000000 ≫ 1

{ }

Braces

set

⌊x⌋

floor brackets

rounds number to lower integer

⌊4.3⌋ = 4

⌈x⌉

ceiling brackets

rounds number to upper integer

⌈4.3⌉ = 5

x!

exclamation mark

Factorial

4! = 1*2*3*4 = 24

x |

vertical bars

absolute value

-5 | = 5

f (x)

function of x maps values of x to f(x)

f (x) = 3x+5

(f ∘ g)

function composition (f ∘ g) (x) = f (g(x))

f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)

(a,b)

open interval (a,b) = {x | a < x < b}

x∈ (2,6)

[a,b]

closed interval

[a,b] = {x | a ≤ x ≤ b}

x ∈ [2,6]

∆

Delta

change / difference

∆t = t1 - t0

∑

Sigma

summation - sum of all values in range of series

∑ xi= x1+x2+…+xn

∑∑

Sigma

double summation

∑+∑

∏

capital pi

product - product of all values in range of series

∏ xi=x1∙x2∙…∙xn

e

Euler’s number

e = 2.718281828…

e = lim (1+1/x)x , x→∞

γ

Euler-Mascheroni constant

γ = 0.5772156649…

φ

golden ratio constant

·

Dot

scalar product

a · b

×

Cross

vector product

a × b

⊗

tensor product

tensor product of A and B

A ⊗ B

[ ]

Brackets

matrix of numbers

|| x ||

double vertical bars

norm

AT

Transpose

matrix transpose

(AT)ij = (A)ji