Sentence examples for true continuum from inspiring English sources

If space is a true continuum, then to describe even something as simple as the distance between two points requires an infinite amount of information, specified by a number with infinitely many decimal places.

But later he radically transformed the concept of "point", endowing points with sufficient fluidity to enable them to serve as generators of a "true" continuum.

In his mature thought, he radically transformed the concept of point, endowing points with sufficient fluidity to enable them to serve as generators of a "true" continuum.

The fact that single points in a true continuum "cannot be exhibited" arises, Weyl asserts, from the fact that they are not genuine individuals and so cannot be characterized by their properties.

Peirce maintained that if "enough" points were to be crowded together by carrying insertion of new points between old to its ultimate limit they would through a logical "transformation of quantity into quality"—lose their individual identity and become fused into a true continuum.

As for the second difference, in our simple example there are but ten distinct experiences, whereas Cinematic realists will insist that on their model we are dealing with a true continuum, in the mathematical sense: we are to suppose that the perceiving of the tennis game involves an infinite number of distinct momentary experiences, not just ten.

Thatcher (2009) has suggested that if the brittle-elastic crust is stronger than the ductile lithosphere then a block model is preferable, while if the opposite is true, then continuum models should be used.

Rock masses in particular are modelled as standard continua, Cosserat equivalent continua and true discontinua formed by discrete blocks.

The abstract entity corresponding to ZFC, for instance, is partial in the sense that it neither makes the continuum hypothesis true nor false.

It follows that the statement $r = 00 \vee r \neq 0)$ does not hold, and therefore that the law of trichotomy $\forall x(x \lt y \vee x=y \vee x \gt y)$ is not true on the intuitionistic continuum.

The question still remains whether, with some axiom system for set theory, the continuum hypothesis is true.