Math letters and symbols

Index

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Greek letters in math and science

This is a copy from the same section in my equation page.
I took this from Wiki  and adjusted it with comments that I find useful.

  Name and use
  Name and use
Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron

Curly d
In partial derivatives
 δ  Kronecker delta
Δ δ= Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi

Line maybe curved as slash /

Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
    Σσ
Sigma

not equal ~ About

Source: Wiki 

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Double-struck capital letters in math

Source: http://xahlee.info/comp/unicode_math_font.html

Meaning in Math

  •  → integers.
  •  → natural numbers.
  •  → primes.
  •  → be rational.
  •  → get real.
  •  → complex number.
  •  → quaternions.
  •  → sedenions.
  •  → imaginary part
  •  → real part
  •  → Derivative
  •  → Differential
  •  → euler’s number (natural growth number)
  •  → imaginary unit.
  •  → notation used by engineers for ⅈ
  •  → cardinality of infinite sets.
  •  → continuum

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Table of set theory symbols

Taken and adapted from www.rapidtables.com

Symbol Symbol Name Meaning /
definition
Example
{ } set a collection of elements A = {3,7,9,14},
B = {9,14,28}
| such that so that A = {x | x\mathbb{R}x<0}
A⋂B intersection objects that belong to set A and set B A ⋂ B = {9,14}
A⋃B union objects that belong to set A or set B A ⋃ B = {3,7,9,14,28}
A⊆B subset A is a subset of B. set A is included in set B. {9,14,28} ⊆ {9,14,28}
A⊂B proper subset / strict subset A is a subset of B, but A is not equal to B. {9,14} ⊂ {9,14,28}
A⊄B not subset set A is not a subset of set B {9,66} ⊄ {9,14,28}
A⊇B superset A is a superset of B. set A includes set B {9,14,28} ⊇ {9,14,28}
A⊃B proper superset / strict superset A is a superset of B, but B is not equal to A. {9,14,28} ⊃ {9,14}
A⊅B not superset set A is not a superset of set B {9,14,28} ⊅ {9,66}
2A power set all subsets of A  
\mathcal{P}(A) power set all subsets of A  
A=B equality both sets have the same members A={3,9,14},
B={3,9,14},
A=B
Ac complement all the objects that do not belong to set A  
A’ complement all the objects that do not belong to set A  
A\B relative complement objects that belong to A and not to B A = {3,9,14},
B = {1,2,3},
A \ B = {9,14}
A-B relative complement objects that belong to A and not to B A = {3,9,14},
B = {1,2,3},
A – B = {9,14}
A∆B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}
A⊖B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}
a∈A element of,
belongs to
set membership A={3,9,14}, 3 ∈ A
x∉A not element of no set membership A={3,9,14}, 1 ∉ A
(a,b) ordered pair collection of 2 elements  
A×B cartesian product set of all ordered pairs from A and B  
|A| cardinality the number of elements of set A A={3,9,14}, |A|=3
#A cardinality the number of elements of set A A={3,9,14}, #A=3
| vertical bar such that A={x|3<x<14}
congruency 3 is cogruent to 15 in modulo 12
(modular arithmetic)
3 ≡ 15 (mod12)
0 aleph-null infinite cardinality of natural numbers set  
1 aleph-one cardinality of countable ordinal numbers set  
Ø empty set Ø = {} A = Ø
\mathbb{U} universal set set of all possible values  
0 natural numbers / whole numbers  set (with zero) \mathbb{N}0 = {0,1,2,3,4,…} 0 ∈ \mathbb{N}0
1 natural numbers / whole numbers  set (without zero) \mathbb{N}1 = {1,2,3,4,5,…} 6 ∈ \mathbb{N}1
integer numbers set \mathbb{Z} = {…-3,-2,-1,0,1,2,3,…} -6 ∈ \mathbb{Z}
rational numbers set \mathbb{Q} = {| x=a/ba,b\mathbb{Z} and b≠0} 2/6 ∈ \mathbb{Q}
real numbers set \mathbb{R} = {x | -∞ < x <∞} 6.343434 ∈ \mathbb{R}
complex numbers set \mathbb{C} = {| z=a+bi, -∞<a<∞,      -∞<b<∞} 6+2i ∈ \mathbb{C}

A agnostic pluralist seeker

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