“infinity”的概念、定义、翻译、参考文献-科学参考

infinity

Physics

Symbol ∞. A quantity having a value that is greater than any assignable value. Minus infinity, −∞, is a quantity having a value that is less than any assignable value. The occurrence of infinities in any calculation of a physical quantity indicates that there is something fundamentally wrong with the theory used to perform the calculation, in accord with the slogan ‘Infinity is not a physical quantity’.

Mathematics

For the real numbers, a value greater than any finite number, denoted by ∞. It is natural to introduce notions of tending to ∞ and –∞, though these are not themselves real numbers. For the complex numbers, it is natural to introduce a notion of a single infinity ∞ to make the extended complex plane.

Science and Technology

A quantity or object that is unbounded. For instance, the series of integers is infinite because there is no number so large that 1 cannot be added to it, and the series of even integers is infinite because there is none so large that 2 cannot be added to it. However, ∞ + ∞ = ∞; ∞ × ∞ = ∞.
Mike Allaby

Philosophy

The unlimited; that which goes beyond any fixed bound. Exploration of this notion goes back at least to Zeno of Elea, and extensive mathematical treatment began with Eudoxus of Cnidus. The mathematical notion was further developed by Cantor and K. T. W. Weierstrass (1815–97) in the 19th century. In the philosophy of space and time problems arise both with the infinitely small (see Bayle’s trilemma, Zeno’s paradoxes) and with the infinitely large or boundless nature that each seems, intuitively, to possess. Kant argued in the antinomies that consistently regarding space or time as either finite or as infinite, was impossible, and this formed a key element in his idealist theory of them as imposed upon an unknown (noumenal) nature by our own forms of sense. Philosophically one important division is between thinkers such as Cantor who can countenance actual completed infinities, and those such as Aristotle or the mathematician Leopold Krönecker (1823–91) who reject any such notion in favour of merely ‘potential’ infinities.

单词	infinity
释义	infinity Physics Symbol ∞. A quantity having a value that is greater than any assignable value. Minus infinity, −∞, is a quantity having a value that is less than any assignable value. The occurrence of infinities in any calculation of a physical quantity indicates that there is something fundamentally wrong with the theory used to perform the calculation, in accord with the slogan ‘Infinity is not a physical quantity’. Mathematics For the real numbers, a value greater than any finite number, denoted by ∞. It is natural to introduce notions of tending to ∞ and –∞, though these are not themselves real numbers. For the complex numbers, it is natural to introduce a notion of a single infinity ∞ to make the extended complex plane. Science and Technology A quantity or object that is unbounded. For instance, the series of integers is infinite because there is no number so large that 1 cannot be added to it, and the series of even integers is infinite because there is none so large that 2 cannot be added to it. However, ∞ + ∞ = ∞; ∞ × ∞ = ∞. Mike Allaby Philosophy The unlimited; that which goes beyond any fixed bound. Exploration of this notion goes back at least to Zeno of Elea, and extensive mathematical treatment began with Eudoxus of Cnidus. The mathematical notion was further developed by Cantor and K. T. W. Weierstrass (1815–97) in the 19th century. In the philosophy of space and time problems arise both with the infinitely small (see Bayle’s trilemma, Zeno’s paradoxes) and with the infinitely large or boundless nature that each seems, intuitively, to possess. Kant argued in the antinomies that consistently regarding space or time as either finite or as infinite, was impossible, and this formed a key element in his idealist theory of them as imposed upon an unknown (noumenal) nature by our own forms of sense. Philosophically one important division is between thinkers such as Cantor who can countenance actual completed infinities, and those such as Aristotle or the mathematician Leopold Krönecker (1823–91) who reject any such notion in favour of merely ‘potential’ infinities.
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