Sentence examples for I implies a from inspiring English sources

For each (A,B>0), it is not true that the condition (I,sigma,A leqslant I,sigma,B) or the condition (A,sigma,I leqslant B,sigma,I) implies (A leqslant B).

A, B ∈ I implies A ∪ B ∈ I, A ∈ I, B ⊂ A implies B ∈ I.

In the thermodynamic limit N → ∞, a vanishing σ ( A ) for I implies a stationary stable state with A ∼ 1 / 2 and no consensus.

∅ ∈ I, A, B ∈ I implies A ∪ B ∈ I, for each A ∈ I and B ⊂ A we have B ∈ I, I is called a nontrivial ideal if X ∈ I ≠ ∅ and P ( X ) is the power set of X.

If X is a non-empty set, then a family of subsets of X is called an ideal in X if and only if (a) ∅ ∈ I,   (b) A, B ∈ I implies A ∪ B ∈ I,   (c) for each A ∈ I and B ⊂ A we have B ∈ I,  .

A nonempty family I ⊂ 2 Y of subsets a nonempty set Y is said to be an ideal in Y if the following conditions hold: (i) A, B ∈ I implies A ∪ B ∈ I ;   (ii) A ∈ I, B ⊂ A imply B ∈ I.  .

Since the addition of e i = (u i, v i ) implies an interaction or functional equivalence between proteins u i and v i, we chose sim(e i ) to be the amount of overlap between the neighborhoods of u i and v i, i.e., sim(e i ) =, where (v i ) denotes a set of neighbors of node v i in the graph.

It's not that national feeling didn't exist before, but nationalism, as I see it, implies a program to make people the same".

∅ ∈ I Open image in new window; A, B ∈ I imply A ∪ B ∈ I Open image in new window and.

A family I ⊆ P ( X ) Open image in new window is said to be an ideal in X if (1) ∅ ∈ I Open image in new window;   (2) A, B ∈ I imply A ∪ B ∈ I Open image in new window and   (3) A ∈ I, B ⊂ A imply B ∈ I Open image in new window.  .

Reduced levels of plastid 16S and/or 5S rRNAs in mutants of group I imply a severe drop in translation rates and consequently a general loss of transcripts synthesized by the PEP.