Sentence examples for implication x from inspiring English sources

James [4] proved that X is a Hilbert space if and only if isosceles orthogonality is homogeneous, i.e., if and only if the implication x ⊥ I y ⇒ x ⊥ I αy holds for each real number α.

Table 1 Dimension of parameters and variables used in simulations Variable or parameter Dimension Implication x, w, y, z Dimensionless Proportional population X, W, Y, Z Hundred thousand Day−1 Population Λ Hundred thousand Day−1 The number of immigration population (beta_{0}) Unity.

More precisely, the implications x ⊥Ry ⇒ x ⊥ B y and x ⊥ R y ⇒ x ⊥ I y hold.

Where specifically noted, therefore, the notation in the left-hand column of Table 1 (Logical expressions) is used in the following, with the particular implication that "X", for example, means "the population group with X including those members with C as well" (i.e. "X + XC" in differential equations terminology).

Then T is said to be demiclosed at v ∈ H if, for any sequence {x n } in C, the following implication holds: x n → u ∈ C, T x n → v i m p l y T u = v, where → (resp. ⇀) denotes strong (resp. weak) convergence.

Then T is said to be demiclosed at v ∈ H if, for any sequence {x n } in C, the following implication holds: x n ⇀ u ∈ C, T x n → v imply T u = v, where → (respectively ⇀) denotes strong (respectively weak) convergence.

Moreover if we suppose that the following implication holds: x ∗, y ∗ ∈ Fix ( T ) ⇒ ( x ∗, y ∗ ) ∈ E ( G ), then Fix ( T ) = S Fix ( T ) = { x ∗ }.

An association rule can be seen as an implication X→Y, with X and Y being sets of items.

The latter generalization is known as "pervasion" (vyāpti; Tibetan khyab pa) of C by B a universally generalized material implication, for all x: if x is C then x is B, with the interesting feature that the quantification ranges over both actual and non-actual items.

Note that neither of the implications P ( x, y, t ) = 1 ⇔ x = y (namely (F2)) necessarily hold, and P is nonsymmetric, i.e., in general, P does not satisfy (F3).

If an instructor says something like "the three most important implications of X are…" or "there are two basic reasons why X happened," then this is likely information that you will want to record in your notes.