Continuum | mathematics | Britannica (original) (raw)
Learn about this topic in these articles:
application in space–time
In space-time …to be a flat, three-dimensional continuum—i.e., an arrangement of all possible point locations—to which Euclidean postulates would apply. To such a spatial manifold, Cartesian coordinates seemed most naturally adapted, and straight lines could be conveniently accommodated. Time was viewed independent of space—as a separate, one-dimensional continuum, completely homogeneous along its… Read More
research of Dedekind
In Richard Dedekind …irrational numbers could form a continuum (with no gaps) of real numbers, provided that the real numbers have a one-to-one relationship with points on a line. He said that an irrational number would then be that boundary value that separates two especially constructed collections of rational numbers. Read More
significance in Zeno’s paradoxes
In Achilles paradox …of the problem of the continuum. Aristotle’s solution to it involved treating the segments of Achilles’ motion as only potential and not actual, since he never actualizes them by stopping. In an anticipation of modern measure theory, Aristotle argued that an infinity of subdivisions of a distance that is finite… Read More
In Western philosophy: Epistemology of appearance …from the problem of the continuum. Although they have often been dismissed as logical nonsense, many attempts have also been made to dispose of them by means of mathematical theorems, such as the theory of convergent series or the theory of sets. In the end, however, the logical difficulties raised… Read More
