Sentence examples for hence finite from inspiring English sources

Methodologies are developed for the estimation of the classification error probability, using the available, hence finite, set of data.

Admittedly overused, the image of "Spaceship Earth" nonetheless powerfully illustrates both that the planet is a discrete, and hence finite, entity and that its occupants cannot escape the consequences of their activity.

This makes it impossible always to determine unique class membership; hence, finite differentiation is not achieved.

The first sum in (26) is a finite sum of finite terms, and is hence finite.

Therefore, for each (gamma in G), (gamma ne 1_G), the set of fixed points ( Fix (gamma )), which is closed, is either discrete (hence finite), or it consists of a discrete set plus a set (the points ( x in Fix (gamma )) where the derivative is the identity) which is open and closed.

The bound given above to ensure and hence finite, gives a new diagnostic.

The answer to this question is positive; hence, finite-net multi-CCS can represent all finite, statically reduced, P/T Petri nets, up to net isomorphism.

So we can assume that (bar{G}) is hereditary just infinite and hence residually finite.

For example, the group in [37] is based on the R. Thompson group V which is infinite and simple (hence not residually finite).

On the other hand,, and hence is finite, so is a finite union of closed sets, hence closed, so.

Then (G/G_{omega }) is residually polycyclic and hence residually finite as every polycyclic group is residually finite [34].