Journal of Humanistic Mathematics 7 (2):355-378 (2017)

Authors
James Franklin
University of New South Wales
Abstract
The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.
Keywords Discrete  Continuous  Philosophy of mathematics  infinitesimals
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References found in this work BETA

Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
Analog and Digital, Continuous and Discrete.Corey J. Maley - 2011 - Philosophical Studies 155 (1):117-131.
Analog and Digital.David K. Lewis - 1971 - Noûs 5 (3):321-327.

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Citations of this work BETA

Finitism in Geometry.Jean-Paul Van Bendegem - 2002 - Stanford Encyclopedia of Philosophy.
The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - “Metafizika” Journal 2 (8):p. 87-100.

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