- function. Euler's
formula states that, for any real number
x, one has e i
x = cos
x + i sin
x , {\displaystyle e^{ix}=\cos
x+i\sin
x,}
where e is the...
- the
values of
x {\displaystyle
x}
satisfying the equation,
called the
roots or zeros, can be
found using the
quadratic formula,
x = − b ± b 2 − 4...
-
x −
x 1 ) (
x −
x 2 ) =
x 2 − (
x 1 +
x 2 )
x +
x 1
x 2 = 0 {\displaystyle \left(
x-
x_{1}\right)\left(
x-
x_{2}\right)=
x^{2}-\left(
x_{1}+
x_{2}\right)
x+
x_{1}x_{2}=0}...
- inserted—to make
formulas easier to read. Thus the
formula: ¬ ∀
x P (
x ) → ∃
x ¬ P (
x ) {\displaystyle \lnot \forall
xP(
x)\to \exists
x\lnot P(
x)}
might be...
-
natural numbers, the
formula "
x+2 > y" is open,
since it
contains the free
variables x and y. In contrast, the
formula "∃y ∀
x:
x+2 > y" is closed, and...
- logic, a
formula is
satisfiable if it is true
under some ****ignment of
values to its variables. For example, the
formula x + 3 = y {\displaystyle
x+3=y} is...
- open
formula. For instance, the
universal quantifier ∀ {\displaystyle \forall } in the
first order formula ∀
x P (
x ) {\displaystyle \forall
xP(
x)} expresses...
- Moivre's
formula (also
known as de Moivre's
theorem and de Moivre's identity)
states that for any real
number x and
integer n it is the case that ( cos
x +...
- f (
x ) d
x ≈ ∑ i = 0 n w i f (
x i ) , {\displaystyle \int _{a}^{b}f(
x)\,dx\approx \sum _{i=0}^{n}w_{i}\,f(
x_{i}),}
where for a
closed formula,
x i =...
- [[]] In science, a
formula is a
concise way of
expressing information symbolically, as in a
mathematical formula or a
chemical formula. The
informal use...
