-
universal quantifier is
encoded as U+2200 ∀ FOR ALL in Unicode, and as \
forall in
LaTeX and
related formula editors.
Suppose it is
given that 2·0 = 0 +...
- ( x , y ) = 0 ) ] {\displaystyle (\
forall x\
forall y\,[\mathop {\leq } (\mathop {+} (x,y),z)\to \
forall x\,\
forall y\,\mathop {+} (x,y)=0)]} is a formula...
- {\displaystyle \
forall A\
forall w_{1}\
forall w_{2}\ldots \
forall w_{n}{\bigl [}\
forall x(x\in A\Rightarrow \exists !y\,\varphi )\Rightarrow \exists B\ \
forall x{\bigl...
- (quantified) type variables. E.g.: cons :
forall a . a -> List a -> List a nil :
forall a . List a id :
forall a . a -> a
Polymorphic types can become...
- {\displaystyle \
forall x_{1}\ldots \
forall x_{n}\;\exists y\;P(y)} with ∀ x 1 … ∀ x n P ( f ( x 1 , … , x n ) ) {\displaystyle \
forall x_{1}\ldots \
forall x_{n}\;P(f(x_{1}...
- < δ ⟹ | f ( x ) − L | < ε ) . {\displaystyle (\
forall \varepsilon >0)\,(\exists \delta >0)\,(\
forall x\in \mathbb {R} )\,(0<|x-p|<\delta \implies |f(x)-L|<\varepsilon...
- \
forall x\ (x+0=x)} ∀ x , y ( x + S ( y ) = S ( x + y ) ) {\displaystyle \
forall x,y\ (x+S(y)=S(x+y))} ∀ x ( x ⋅ 0 = 0 ) {\displaystyle \
forall x\...
- ( x , w 1 , … , w n , A ) ] ) {\displaystyle \
forall w_{1},\ldots ,w_{n}\,\
forall A\,\exists B\,\
forall x\,(x\in B\Leftrightarrow [x\in A\land \varphi...
- {\begin{aligned}\
forall x,p(x)\to (\
forall y,q(x)\to \pm r(x,y)),&\quad \
forall x,p(x)\to (\exists y,q(x)\wedge \pm r(x,y))\\\exists x,p(x)\wedge (\
forall y,q(x)\to...
- \land \ \lnot \exists n\ \ (n\in o))\ \land \ \
forall x\ (x\in I\Rightarrow \exists y\ (y\in I\ \land \ \
forall a\ (a\in y\Leftrightarrow (a\in x\ \lor \ a=x)))))...
