Sentence examples for power sets of from inspiring English sources
We denote the power sets of U by P ( U ). Then soft sets are defined as follows.
Then a family of sets I ⊆ 2 X (power sets of X) is said to be an ideal if I is additive, i.e., A, B ∈ I ⇒ A ∪ B ∈ I and hereditary, i.e., A ∈ I, B ⊆ A ⇒ B ∈ I.
These can be taken to be the axioms of Z (other than extensionality and choice, which are not needed): the sethood of pairs of sets, unions of sets, power sets of sets, and the existence of an infinite set are enough to give us the world of ZFC.
A family of sets (I subseteq2^{A}) (power sets of A) is an ideal if I is additive, i.e. (S, T in I Rightarrow S cup T in I), and hereditary i.e. (S in I), (T subseteq S Rightarrow T in I), where A is any non-empty set.
A family of sets I ⊂ P ( N ) (power sets of ℕ) is called an ideal if and only if for each A, B ∈ I, we have A ∪ B ∈ I, and for each A ∈ I and each B ⊂ A, we have B ∈ I.
Two operators both denoted by ′ can be defined on the power sets of objects 2 G and attributes 2 M as follows: ′ : 2 G → 2 M, X ′ = { m ∈ M | ∀ g ∈ X, (g, m ) ∈ I } The ′ operator is dually defined on attributes.
Post hoc tests showed a power setting of 0.5 J/80 Hz was significantly more efficient than low-power settings 0.2 J/50 Hz and 0.5 J/20 Hz (p < 0.05).
Increasing the microwave power setting of MATS system amplified the temperature alteration.
A Latin power set of cardinalitym ≥ 2 is a set of Latin squares { A, A2, A3,...,Am }.
This can be followed by iterating the power set operation as before: Aω′ is the power set of Aω and so forth.
The bottom of the hierarchy is composed of the sets A0 = Ø, A1, …, An, …, in which each An + 1 is the power set of the preceding An.
