To each value of x there correspond a finite number of values of y.
Our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a "dimension function" from β × β into N ∪.
In particular, to every number β of Λ, different from its possible maximum, there corresponds the smallest element in Λ that is greater than β.
To these external questions there correspond, Carnap claimed, no propositions with truth values; to no such question, for example, is there a true answer of the form: "Yes, infinitely many abstract numbers exist".
That is, the key to his program is that for every word in the dictionary and every sentence in the language there corresponds a unique predicate that is true of just the tokens of that word/that sentence.
Formations are contents that enter into consciousness through carrying out specific functions in the sense that to every class and subclass of acts there corresponds a certain content specific to each and every act.
We say that a semi-inner-product is defined on, if to any there corresponds a real number denoted by satisfying the following properties: (s1) for, (s2) for, and, (s3) for, (s4).
Generalising this idea we say that to every subset A of a system's phase space there corresponds a property PA so that the system possesses that property at time t iff the system's state x is in A at t.
Weights are given by the parameters wj (see equations following eq. (1)), which denote the relative strength of the modified synapses with respect to the baseline, to which there corresponds the value 〈w〉 = 1.
