"That's what I've always wanted that it's not partial.
After learning that Whitman is "not partial to strawberries," the reader is next confronted with sacks of rats.
This is an especially good idea if your parrot is not partial to vegetables!
The natural audience for talking-to-God television is not immune to humor, but it probably isn't partial to oral sex jokes.
For example, if X = R is the set of real numbers, d ( x, y ) = | x − y |, q = 2 and a = 3, then p b ( x, y ) = ( x − y ) 2 + 3 is a partial b-metric on X with s = 2 2 − 1 = 2, but it is not a partial metric on X.
The condition just sketched in the antecedent is fundamental: without it, a sentence p might very well have been an expression of a judgment j once (j was a partial cause of p), but no meaning is linked with p: for, if p is incomprehensible, namely it is not a partial cause of another judgment j′, then nothing can be said to be its meaning (§31).
Then ⪯ is a preorder, but it is not a partial order since it fails to be antisymmetric.
The binary relation ≼ is a preorder on X, but it is not a partial order on X. 2.
( P 1 ) The binary relation ≼ is a preorder on X (reflexive and transitive), but it is not a partial order since 2 ≼ 3, 3 ≼ 2 and 2 ≠ 3. Furthermore, if x, y ∈ X and x ≼ y, then x ∈ I ⇔ y ∈ I ; x ∈ { 2, 3 } ⇔ y ∈ { 2, 3 } ; x ∈ { 4, 5, 6, 7 } ⇒ y = x.
T is not a d-contraction (that is, there is no k ∈ [ 0, 1 ) such that d ( T x, T y ) ≤ k d ( x, y ) for all x, y ∈ X ) because d ( T 4, T 5 ) = d ( − 1, 1 ) = 2, but d ( 4, 5 ) = 1. . The binary relation ≼ is a preorder on X, but it is not a partial order on X. The measure mapping d does not hold any of the four classical properties ( M 1 )-( M 4 ) that define a metric space.
