Sentence examples for be the inverse element from inspiring English sources

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

∀x ∈G and let x−1 be the inverse element of x.

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

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

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.

(Existence of inverse elements) The operator δ has the inverse operator (delta^{-1}:Pi^times mathbb{T}^rightarrow mathbb{T}^) and (delta^{-1} tau,t)= delta^{-1} tau},t)), where (tau^{-1}in Pi^) is the inverse element of τ. (Existence of identity element) (e_{Pi^ in Pi^) and (delta (e_{Pi^,t)=t) for any (tin mathbb{T} ^), where (e_{Pi^) is the ideltaty element in (Pi^).

((P_{2})):  (Existence of inverse elements) The operator δ has the inverse operator (delta^{-1}:Pi^times mathbb{T}^rightarrow mathbb{T}^) and (delta^{-1} tau,t)= delta^{-1} tau},t)), where (tau^{-1}in Pi^) is the inverse element of τ. ((P_{3})):  (Existence of identity element) (e_{Pi^ in Pi^) and (delta (e_{Pi^,t)=t) for any (tin mathbb{T} ^), where (e_{Pi^) is the ideltaty element in (Pi^).

The integer b is called the inverse element of the integer a and is denoted −a.

Or it can be the inverse.

Finally, the inverse of a/b is b/a, therefore the axiom of the inverse element is satisfied.

Notice that although in monoids we are not allowed to apply the inverse element x − 1, by the meaning of functions, we can use this inverse element as a fractal of the form 1 S 0 1 ( x ).