Sentence examples for implies by definition from inspiring English sources

Such careless terminology denies the very essence of music as a temporal art, which implies by definition the omnipresence of rhythm as "order in musical time".

(a By Lemma 2.3(1), and are u.h.c., which implies by Definition 2.1(2) and Remark 2.2(1) that for each, is u.s.c.s.c

If is separable and reflexive and has property, then it has property as well and this implies by definition that also has property.

Then we have p x,x =lim_{nrightarrow+infty }p x,x_{n}), which implies, by definition, that ({x_{n}}) converges to (x in X) also in ((X,p)).

From Remark 2.9,, which implies by Definition 2.4(2) that is a Cauchy sequence in which is a closed subset of the complete cone metric space and hence is complete.

Improved oxygenation implies, by definition, improvement of the ventilation/perfusion ratio.

The left action is not free in general, since it is possible to have (g(xv =xv) for all (vin X^*) and for a non-trivial element (gin G), which will imply, by definition of the left action, that (gcdot x=x).

Let us suppose now that the substitution in the clause THEN in Op_Fired_Idtransion contains a multisets overload and is executed and let us prove that operation Op_Fired_Idtransion is executed (reverse implying): by definition, an operation is executed if and only if the THEN substitution of this operation is executed.

Ethnoprimatological studies imply, by definition, that primates are particularly worthy subjects of research in the studied culture [Fuentes, 2012], but this assumption needs to be critically examined, particularly in ethnoprimatology sensu stricto.

Saaty stated that the relative measurement of alternatives in the AHP implied by definition that all included alternatives were relevant, in contrast to utility theory that could face rank reversal problems [ 115].

which implies, by the definition of y k, that lim k → ∞ ∥ y k − x k ∥ = 0, (3.8).