Composable Math Markup (CMath)

Symbols

Arithmetic

Basic:

•   	Plus sign
  

• − [-] Minus sign

• × Multiplication ÷ [d] Division / ⁄ [/] Fraction slash

Technical: ± [+-] Plus-minus sign ∕ [d/] Division slash ⋅ [.] Multiplication or dot product √ [root] Square root - or [2rt]? ∛ [3root] Cube root - or [3rt]? ∜ [4root] Fourth root - or [4rt]? ∞ [inf] Infinity ∶ [:] Ratio ∷ [::] Proportion sum ∑ [sum] Sum prod ∏ [prod] Product 𝔼 [expect] Expected value pi π [pi] Mathematical value pi (3.141…)

Comparison

Basic: = = Equals ≠ [/=] Not equal to < < Less-than

  Greater-than

<= ≤ [<=] Less-than or equal to - or [le]?

= ≥ [>=] Greater-than or equal t - or [ge]?

Technical: ≪ [«] Much less-than ≫ [»] Much greater-than ≈ [] Almost equal to ≉ [/] Not almost equal to ≊ [~=] Almost equal or equal to ≮ [/<] Not less-than ≯ [/>] Not greater-than ≰ [/<=] Not less-than or equal to ≱ [/>=] Not greater-than or equal to ≶ [<>] Less-than or greater-than ≷ [><] Greater-than or less-than ≸ [/<>] Not less-than or greater-than ≹ [/><] Not greater-than or less-than ≉ [/~~] Almost equal to ≝ [def=] Equal by definition ∝ [prop] Proportional to

Logical

Basic: ¬ [not] Not sign ∧ [and] Logical and ∨ [or] Logical or

Technical: ⊕ [(+)] Exclusive or ⊻ [xor] Exclusive or ⊼ [nand] Not and ⊽ [nor] Not or → [–>] Logical implication (single arrow) ⇒ [==>] Logical implication (double arrow) ↔ [<->] Logical if-and-only-if (single arrow) ⇔ [<=>] Logical if-and-only-if (double arrow) ∀ [all] For all ∃ [ex] There exists ∄ [/ex] There does not exist

Deduction: ⊤ [top] Unconditional truth ⊥ [bot] Unconditional falsity ⊢ [|-] Syntactic entailment ⊨ [|=] Semantic entailment ∎ [qed] End of proof

Set operators

∪	[un]	Union
∩	[int]	Intersection
∁	[com]	Complement
∖	[set-]	Set minus	or [\]?

Set comparison

∅	[0]	Empty set
∈	[in]	Element of
∉	[/in]	Not element of
∋	[con]	Contains
∌	[/con]	Does not contain
⊂	[sub]	Subset of
⊃	[sup]	Superset of
⊆	[sub=]	Subset of or equal to
⊇	[sup=]	Superset of or equal to
⊄	[/sub]	Not a subset of
⊅	[/sup]	Not a superset of
⊈	[/sub=]	Not a subset of or equal to
⊉	[/sup=]	Not a superset of or equal to

Vulgar fraction characters

½	[1/2]
⅓	[1/3]
⅔	[2/3]
¼	[1/4]
¾	[3/4]
...

Matrices

⋅	[.]	Dot product

Standard mathematical sets

𝔹	[B]	Booleans
ℕ	[N]	Natural numbers
ℤ	[Z]	Integers
ℚ	[Q]	Rational numbers
ℝ	[R]	Real numbers
ℂ	[C]	Complex numbers
ℍ	[H]	Hamiltonion quaterions

Tuples

X	[<],[o<>]	Open mathematical angle bracket
X	[>],[c<>]	Close mathematical angle bracket

<[a,b,c]> Tuple of a,b,c

Functions

→	[-->]	Function mapping set/type X to set/type Y
↦	[|->]	Function mapping element x to element y

Mathematical Spacing and Punctuation

" "	[_]	Medium mathematical space

Basic mathematics

Infix operators

x+y x-y x*y x/y x mod y x^y x to the power y

frac[x/y] Fraction x over y

root[x] Square root of x root(n)[x] nth root of x √[x] Square root of x ∛[x] Cube root of x ∜[x] Fourth root of x

log[x] Base-10 logarithm of x log(k)[x] Base-k logarithm of x ln[x] Base-e logarithm of x

ceil[x] Ceiling of x floor[x] Floor of x

N-ary inequalities: x < y < z etc.

[x..y] Closed interval from x to y [x<..<y] Open interval from x to y exclusive [x<..y] Half-open interval from x (exclusive) to y (inclusive) [x..<y] Half-open interval from x (inclusive) to y (exclusive) or: [x..y] Closed interval from x to y [>x..y<] Open interval from x to y exclusive [>x..y] Half-open interval from x (exclusive) to y (inclusive) [x..y<] Half-open interval from x (inclusive) to y (exclusive)

Transcendental functions

Circular: sin cos tan arcsin arccos arctan csc sec cot arccsc arcsec arccot

Hyperbolic: sinh cosh tanh csch sech coth arcsch arsech arcoth

Probability and combinatorics

choose[x y]		x choose y
expect[x]		expected value of x
𝔼[x]			expected value of x

Modular integer arithmetic

Z/[m]			the integers modulo m
ℤ/[m]			the integers modulo m
x ≡ y mod m		x is congruent to y modulo m

Programming logical operators

&& Logical and || Logical or ! Logical not

Programming bitwise operators

~ Bitwise not & Bitwise and ~& Bitwise nand | Bitwise or ~| Bitwise nor « Bitwise left shift

  	Bitwise right shift