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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."
InfinityThe attempt to avoid a direct affirmation about infinite parallel stra — Infinity
"The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. ...Simplicius cites others who worked on the problem and says further that people "in ancient times" objected to the use of the parallel postulate."
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."
InfinityQuote
"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."
InfinityQuote
"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."
InfinityQuote
"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