- mathematics, a
function from a set
X to a set Y ****igns to each
element of
X exactly one
element of Y. The set
X is
called the
domain of the function...
-
inverse element generalises the
concepts of
opposite (−
x) and
reciprocal (1/
x) of numbers.
Given an
operation denoted here ∗, and an
identity element denoted...
-
element in the
lattice Primitive element (coalgebra), an
element X on
which the
comultiplication Δ has the
value Δ(
X) =
X⊗1 + 1⊗
X Primitive element (free...
-
reflexive (which
means that
x ≤
x {\displaystyle
x\leq
x} is true for all
elements x {\displaystyle
x} ),
every element x {\displaystyle
x} is
always comparable...
- such that, for
every element y of the function's codomain,
there exists at
least one
element x in the function's
domain such that f(
x) = y. In
other words...
-
generated by
x {\displaystyle
x} .
Equivalent to
saying an
element x {\displaystyle
x}
generates a
group is
saying that ⟨
x ⟩ {\displaystyle \langle
x\rangle...
- description: it
sends each
element y ∈ Y {\displaystyle y\in Y} to the
unique element x ∈
X {\displaystyle
x\in
X} such that f(
x) = y. As an example, consider...
- In mathematics, an
element x {\displaystyle
x} of a ring R {\displaystyle R} is
called nilpotent if
there exists some
positive integer n {\displaystyle...
-
subfield E(
x)
generated by an
element x, as above, is an
algebraic extension of E if and only if
x is an
algebraic element. That is to say, if
x is algebraic...
-
homogeneous elements x, y we have y
x = ( − 1 ) |
x | | y |
x y , {\displaystyle yx=(-1)^{|
x||y|}xy,}
where |
x|
denotes the
grade of the
element and is 0 or 1...
