Formula Help

Bytes & Parses

⋅
· ·
\(\cdot\) \(\cdot\)
\(\cdot\!\) \(\cdot\!\)
 
∈
ε ε
\(\in\) \(\in\)
\(\in\!\) \(\in\!\)
\(\epsilon\) \(\epsilon\)
\(\epsilon\!\) \(\epsilon\!\)
\(\varepsilon\) \(\varepsilon\)
\(\varepsilon\!\) \(\varepsilon\!\)
 
η η
\(\eta\) \(\eta\)
\(\eta\!\) \(\eta\!\)
 
θ θ
\(\theta\) \(\theta\)
\(\theta\!\) \(\theta\!\)
\(\vartheta\) \(\vartheta\)
\(\vartheta\!\) \(\vartheta\!\)
 
χ χ
\(\chi\) \(\chi\)
\(\chi\!\) \(\chi\!\)


x = xJ = ¢(J) = J¢ = J ¢ = J¢ = J ¢

x = xJ = ¢(J) = J¢ = J ¢ = J¢ = J ¢

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New

W : ( [ Bn ] [ Bk ] )     ( [ Bn × Dn ] [ Bk × Dk ] ) .
Concrete type \(\epsilon\) : ( U X ) ( EU X )
Abstract type \(\epsilon\) : ( [Bn] [Bk] ) ( [Bn × Dn] [Bk] )
Concrete type W : ( U X ) ( EU dX )
Abstract type W : ( [Bn] [Bk] ) ( [Bn × Dn] [Dk] )
\(\epsilon\)F : ( EU X EX ) \(\cong\) ( [Bn × Dn] [Bk] [Bk × Dk] )
WF : ( EU dX EX ) \(\cong\) ( [Bn × Dn] [Dk] [Bk × Dk] )

Old

W : ( [ Bn ] [ Bk ] )     ( [ Bn × Dn ] [ Bk × Dk ] ) .
Concrete type \(\epsilon\) : ( U X ) ( EU X )
Abstract type \(\epsilon\) : ( [Bn] [Bk] ) ( [Bn × Dn] [Bk] )
Concrete type W : ( U X ) ( EU dX )
Abstract type W : ( [Bn] [Bk] ) ( [Bn × Dn] [Dk] )
\(\epsilon\)F : ( EU X EX ) \(\cong\) ( [Bn × Dn] [Bk] [Bk × Dk] )
WF : ( EU dX EX ) \(\cong\) ( [Bn × Dn] [Dk] [Bk × Dk] )

Epitext

Rosebud
Rosebud
Rosebud

Gallery

‹ ›

〈 〉

( )

( , )


A = {ai} = {a1, …, an}
A = 〈A〉 = 〈a1, …, an〉= {‹a1, …, an›}
A^ = (A → B)
A = [A] = [a1, …, an]


dA = {dai} = {da1, …, dan}
dA = 〈dA〉 = 〈da1, …, dan〉= {‹da1, …, dan›}
dA^ = (dA → B)
dA = [dA] = [da1, …, dan]


EA = A ∪ dA = {ai} ∪ {dai} = {a1, …, an, da1, …, dan}
EA = 〈EA〉 = 〈a1, …, an, da1, …, dan〉= {‹a1, …, an, da1, …, dan›}
EA^ = (EA → B)
EA = [EA] = [a1, …, an, da1, …, dan]


X = {xi} = {x1, …, xn}
X = 〈X〉 = 〈x1, …, xn〉= {‹x1, …, xn›}
X^ = (X → B)
X = [X] = [x1, …, xn]


dX = {dxi} = {dx1, …, dxn}
dX = 〈dX〉 = 〈dx1, …, dxn〉= {‹dx1, …, dxn›}
dX^ = (dX → B)
dX = [dX] = [dx1, …, dxn]


X = {xi} = {x1, …, xn}
X = 〈X〉 = 〈x1, …, xn〉= {‹x1, …, xn›}
X^ = (X → B)
X = [X] = [x1, …, xn]


f : Bk → B

f : Bn → B

f–1

Pow(X) = 2X

Arbitrary Bn → B X → B
Basic ¸> Bn ¸> B X ¸> B
Linear +> Bn +> B X +> B
Positive ¥> Bn ¥> B X ¥> B
Singular ××> Bn ××> B X ××> B

The linear propositions, {hom : Bn → B} = (Bn +> B), may be expressed as sums of the following form:

\[\textstyle \sum_{i=1}^n e_i = e_1 + \ldots + e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = 0.\]

The positive propositions, {pos : Bn → B} = (Bn ¥> B), may be expressed as products of the following form:

\[\textstyle \prod_{i=1}^n e_i = e_1 \cdot \ldots \cdot e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = 1.\]

The singular propositions, {x : Bn → B} = (Bn ××> B), may be expressed as products of the following form:

\[\textstyle \prod_{i=1}^n e_i = e_1 \cdot \ldots \cdot e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = (a_i) = \lnot a_i.\]

I = {1, …, n}.

JI

J ⊆ I

AJ

AJ

lJ : Bk → B

\(\ell_J : \mathbb{B}^k \to \mathbb{B}\)

θ : (Kn → K) → K

\(\theta\) : (Kn → K) → K

\(\theta\!\) : (Kn → K) → K

\(\vartheta\) : (Kn → K) → K

\(\vartheta\!\) : (Kn → K) → K

\(\chi\!\) : X → \(\bigcup_x \ \chi_x\!\)

\(\chi\!\) : Kn → ((Kn → K) → K)

\(\chi\!\) : (Kn → K) → (Kn → K)

\(\cong\)

\(\lceil x \rceil\)

xi(x) χ(xLi) \(\lceil x \in L_i \rceil\) Li(x)
xi(x) \(\chi (x \in L_i)\) \(\lceil x \in L_i \rceil\) Li(x)
‹0, 0, 0› ‹0, 0, 0›
‹0, 0, 1› ‹0, 0, 1›
‹0, 1, 0› ‹0, 1, 0›
‹0, 1, 1› ‹0, 1, 1›
‹1, 0, 0› ‹1, 0, 0›
‹1, 0, 1› ‹1, 0, 1›
‹1, 1, 0› ‹1, 1, 0›
‹1, 1, 1› ‹1, 1, 1›