The relation Eω ~ Eϑ defined to hold if \̃gyEω = \̃gyEϑ for every ψ is an equivalence relation.
In Gentzen's proof theory for classical logic, a notion of consequence is defined to hold between multiple premises and multiple conclusions.
The neighborhood-pair relation R r, d, is defined to hold when the distance between the roots of two neighborhood subgraphs of radius r is exactly equal to d.
"What we do in this moment — it will determine whether we let that reality define us, to hold us back, or to inspire us, to push to do what we know is hard".
If (a,b,cin X,) define ([a,c,b]_T) to hold just in case (cin [d,a]_Ocup [d,b]_O) for every common lower bound (d) of (a,b).
Again we start with a connected topological space (X,) but we now define ([a,c,b]_Q) to hold for (a,b,cin X) just in case either (cin {a,b}) or (a) and (b) lie in different quasicomponents of (X{setminus }{c}.) This is the Q-interpretation of betweenness in a connected topological space, and is generally more restrictive than the C-interpretation.
We now start with a continuumwise connected topological space (X,) and define ([a,c,b]_K) to hold for (a,b,cin X) just in case either (cin {a,b}) or (a) and (b) lie in different continuum components of (X{setminus }{c}.) This is the K-interpretation of betweenness in a continuumwise connected topological space, and is generally less restrictive than the C-interpretation.
For every double mutant u Δ v Δ, we represent its logistic function parameters in a triple Ψ u, v = (Ψ u, v (1 ), Ψ u, v (2 ), Ψ u, v (3 ) ) and define Ψ to hold the parametrized logistic function representation over all possible double mutants: Ψ = (Ψ (1 ), Ψ (2 ), Ψ (3 ) ).
Traditionally, holding costs are defined to compensate for the interest of capital tied up in inventory.
However, if we modify the Birkhoff interpretation by defining ([a,c,b]_O) to hold just in case (([a,c,b]_Pvee (c=a)vee (c=b))) does (where (vee ) is logical disjunction), then we clearly have an R-relation whose collection of order intervals of the form ([a,b]_O:=[a,b]_Pcup {a,b}) provides an inducing road system.
Their suggestion for threading this needle is not for policies that restrict private provision of education, but rather for governments to define clear regulations to hold all participants in the education sector accountable.
