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"Empedocles holds that the corporeal elements are four, while all the elements-including those which initiate movement-are six in number; whereas Anaxagoras agrees with Leucippus and Democritus that the elements are infinite."
InfinityGreek mathematical thought does, indeed deal first and last with diffe — Infinity
"Greek mathematical thought does, indeed deal first and last with different kinds of numbers. Were it otherwise, how would it be possible to come to terms with the limitlessness of the material with which arithmetic is confronted? Therefore... theoretical arithmetic... attempts to comprehend all possible groupings of monads in general under arrangements which are determinate, i.e., which possess unambiguous characteristics and which may, in turn, be reduced to their own ultimate elements... Now the most comprehensive eide, those which come closest to the rank of and are therefore termed "the very first"... are the odd and the even. ...each of these halves nevertheless comprising an unlimited multitude of numbers. But each of these... is now in turn gathered "into one"... by means of certain unambiguous characteristics..."
Infinity
Infinity
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Infinity is something which is boundless, limitless, or endless. It is denoted by ∞, called the infinity symbol.
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"Ford, there’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet they’ve worked out."
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"The physicists... always regard the infinite as an attribute of a substance which is different from it and belongs to the class of the so-called elements--water or air or what is intermediate between them. Those who make them limited in number never make them infinite in amount. But those who make the elements infinite in number, as Anaxagoras and Democritus do, say that the infinite is continuous by contact-compounded of the homogeneous parts."
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"The science of nature is concerned with spatial magnitudes and motion and time, and each of these at least is necessarily infinite or finite, even if some things dealt with by the science are not, e.g. a quality or a point--it is not necessary perhaps that such things should be put under either head. Hence it is incumbent on the person who specializes in physics to discuss the infinite and to inquire whether there is such a thing or not, and, if there is, what it is. The appropriateness to the science of this problem is clearly indicated. All who have touched on this kind of science in a way worth considering have formulated views about the infinite, and indeed, to a man, make it a principle of things."
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"All things were together, infinite both in number and in smallness; for the small too was infinite."
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"Dans chaque point réel, qui fait une Monade... il y pourroit lire encor tout le passé, et même tout lavenir infiniment infini, puisque chaque moment contient une infinité de choses , et quil y a une infinité de momens dans chaque partie du temps, et une infinité dheures, dannées, de siecles, deônes, dans toute léternité future. Quelle infinité dinfinités infiniment répliquée, quel monde, quel univers dans quelque corpuscule quon pourroit assigner."
Infinity