law of continuity

In addition, the Law of Continuity can be applied to conceptual computational abstract ideas.

See also Law of Continuity.

Robinson argued that this law of continuity of Leibniz's is a precursor of the transfer principle.

A mathematical implementation of the law of continuity is provided by the transfer principle in the context of the hyperreal numbers.

The hyperreals implement an infinitesimal-enriched continuum and the transfer principle implements Leibniz's law of continuity.

The law of continuity implies the grouping together of objects that have the same trend of motion and are therefore on the same path.

An incipient form of a transfer principle was described by Leibniz under the name of "the Law of Continuity".

Kepler was one of the pioneers of the mathematical applications of infinitesimals, see Law of Continuity.

The hyperreal numbers satisfy the transfer principle, a rigorous version of Leibniz's heuristic Law of Continuity.

It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of non-standard analysis).

Robinson's transfer principle is a mathematical implementation of Leibniz's heuristic law of continuity, while the standard part function implements the Leibnizian transcendental law of homogeneity.

The Law of Continuity is a heuristic principle introduced by Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler.

As turned out to be the case with another such (the so-called law of continuity), they involve matters which, in contemporary terms, are subject to much debate and analysis (respectively on determinism and extensionality).

Law of Continuity-The law of continuity states that elements of objects tend to be grouped together, and therefore integrated into perceptual wholes if they are aligned within an object.

Mr. Burns may at last have developed a vague sense of who "this Homer Simpson" is, but animation does not enforce the laws of continuity and causality with too much rigor.

It appears as an axiom in the works of Gottfried Leibniz (New Essays, IV, 16) and Isaac Newton, the co-inventors of the infinitesimal calculus (see Law of Continuity).

A mathematical implementation of both the law of continuity and infinitesimals was achieved by Abraham Robinson in 1961, who developed non-standard analysis based on earlier work by Edwin Hewitt in 1948 and Jerzy Łoś in 1955.

Though no evidence worth anything has as yet, in my opinion, been advanced in favour of a living being, being developed from inorganic matter, yet I cannot avoid believing the possibility of this will be proved some day in accordance with the law of continuity.

De continuitatis lege et eius consectariis pertinentibus ad prima materiae elementa eorumque vires dissertatio (1754) (A dissertation on the law of continuity and its consequences pertaining to the first elements of matter and of its powers)