2017
DOI: 10.5642/jhummath.201702.18
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Discrete and Continuous: A Fundamental Dichotomy in Mathematics

Abstract: SynopsisThe 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 … Show more

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Cited by 5 publications
(2 citation statements)
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“…Continuity connotes unity; discreteness, plurality" [5]. In addition to mathematical definitions and philosophical considerations [6], applied mathematics adds a pragmatic perspective: in many cases, organizational, practical, or technical conditions determine whether a variable can be considered discrete or continuous. This article does not make a strict distinction between continuous and discrete, but uses both interpretations in parallel.…”
Section: Related Work: the Autoregressive Modelmentioning
confidence: 99%
“…Continuity connotes unity; discreteness, plurality" [5]. In addition to mathematical definitions and philosophical considerations [6], applied mathematics adds a pragmatic perspective: in many cases, organizational, practical, or technical conditions determine whether a variable can be considered discrete or continuous. This article does not make a strict distinction between continuous and discrete, but uses both interpretations in parallel.…”
Section: Related Work: the Autoregressive Modelmentioning
confidence: 99%
“…Çalışmanın odak noktasını oluşturan ayrık paradigması (discrete paradigm), 2000'lerin başından itibaren popülerliğini koruyan parametrik tasarım anlayışına karşı bir eleştiri olarak ortaya çıkmıştır (Sanchez, 2016). Franklin (2017) tarafından aralıksız bir bütün oluşturan öğeler arasındaki ilişki olarak tanımlanan süreklilik kavramı; son 20 yıldır dijital mimariyi yönlendirmiş olup üretim ve ölçeklenebilirlik problemlerine karşı geçerli bir yanıt üretememiştir. Bu anlamda, ayrık paradigma hem hesaplamalı yaklaşım hem de fiziksel ve robotik birleşim için birtakım yenilikler hedefler .…”
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