Sentence examples for inverse element from inspiring English sources

Note that if g is a group element corresponding to a strut or cable, then the inverse element g-1 also corresponds to the same cable or strut.

Moreover, the inverse element of any (x, a) ∈ G1 × G2 is (y, b) ∈ G1 × G2 if and only if y is the inverse element of x in G1 and b is the inverse element of a in G2.

Then x−1 is the inverse element of x in G1 and a−1 is the inverse element of a in G2.

Let (x−1, a−1) be the inverse element of (x, a) in G1 × G2.

where c-1 is the inverse element of c. Proposition 1.

Further, to have an inverse element can also be important in a semigroup.

In the following, we assume that ((mathbb{T},Pi,F,delta)) is a bi-direction matched space, then all the elements from (Pi^) have the corresponding inverse elements in (Pi^).

However, all the elements from (Pi_{1}^backslash {1}) and (Pi_{2}^backslash {1}) have no corresponding inverse elements in (Pi_{1}^) and (Pi_{2}^), respectively, that is, ((Pi_{1}^, tilde{delta }_{1})) and ((Pi_{2}^,tilde{delta }_{2})) are not Abelian groups but they can guarantee the complete closedness of time scales (mathbb{T}_{1}) and (mathbb{T}_{2}).

Two important consequences of the group axioms are the uniqueness of the identity element and the uniqueness of inverse elements.

Furthermore, the inverse elements of the left-hand-side of these MME are identical to the corresponding inverse elements of equation (23).

For example, the group structure may be replaced with a semi-group, meaning that the inverse-element condition is eliminated to explore irreversible time evolution, another characteristic feature that one hopes to capture via classical statistical mechanics.