Sentence examples for be the binary relation from inspiring English sources

Let ⊲ be the binary relation on X defined by ( x, y ) ∈ X × X, x ⊲ y ⟺ x ⪯ y or y ⪯ x.

Let ≽ k be the binary relation on R k, which is defined as: x ≽ k y whenever ∥ x ∥ ≥ ∥ y ∥ for x, y ∈ R k.

Let ≼ be the binary relation on (mathbb{R}) given by xpreccurlyeq y quadLeftrightarrow quad (x=y mbox{ or } x< y leqslant0).

For \(U \subseteq A\), let \(R\) be the binary relation on \(A + A = A \times \{0\} \cup A \times \{1\}\) given by It can be checked that \(R\) is an equivalence relation.

In fact, this partial order can be induced on any nonempty subset (Asubseteqmathbb{R}). Let ≼ be the binary relation on (mathbb{R}) given by xpreccurlyeq y quad Leftrightarrowquad (x=y text{ or } x< yleq0 ).

Let (X= [ 0,infty ) ) and let define (T,g Xrightarrow X) by (gx=x+3) and (Tx=x+4) for all (xin X). Let (mathcal{S}) be the binary relation on X given by (x,mathcal{S},y) if 3leq xleq y quad text{or}quad ( x,y ) in bigl{ (0,1),(1,0),(1,2) bigr}.

For simplicity, we will write x ≼ y if ( x, y ) ∈ R, and we will say that ≼ is the binary relation.

The formal language of set theory is the first-order language whose only non-logical symbol is the binary relation symbol $\in $

For simplicity, we denote if ((x,y in mathcal{R}), and we will say that is the binary relation on X.

That is, it is the binary relation: {<a, b>  |  M   ⊨   φ u, v, w, x, Y, Z) [a, b, c, d, E, F]} Obviously, this concept can be generalized to the situation where a k-ary relation is defined from any particular number of parameters.

Given (z_{0}in X), the mapping T is -nonincreasing-continuous at (z_{0}) if and only if it is -right-continuous at (z_{0}); T is -nonincreasing-continuous if and only if T is -right-continuous; T is -admissible if and only if T is -nondecreasing; The binary relation is transitive on (g(X)) if and only if is g-transitive.