Dictionaries

Russell published in the American Journal of Mathematics, vol. XXX, under the title Mathematical Logics as Based on the Theory of Types, a memoir in which he relies on considerations quite similar to those which precede. After recalling some of … Read More

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We must not forget the preceding considerations when defining the cardinal number. If we consider two collections, we may seek to establish a law of correspondence between the objects of these two collections, so that any object of the first … Read More

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Can the ordinary rules of logic be applied without change, as soon as we consider collections taking an infinite number of objects? This is a question we did not ask at first, but we were led to examine when the … Read More

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I would like to add a remark which relates only indirectly to the foregoing; we have seen above the importance of the Analysis Situs and I explained that this is the real domain of geometric intuition. Does this intuition exist? … Read More

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But the question can be asked from a completely different point of view. We have so far placed ourselves in a purely subjective, purely psychological or, if you will, physiological point of view; we have only considered the relations of … Read More

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It seems, therefore, that space cannot be constructed by considering sets of simultaneous sensations, which must be considered as sequences of sensations. Always go back to what I said before. Why do certain changes appear to us as changes of … Read More

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The question seems resolved; we seem to have only to apply this rule, either to the physical continuum, which is the coarse image of space, or to the corresponding mathematical continuum which is its refined image and which is the … Read More

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But what is a continuum with n dimensions; how does it differ from a continuum whose number of dimensions is larger or smaller? First, let us recall some results recently obtained by the students of Cantor. It is possible to … Read More

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Geometers usually distinguish two kinds of geometries, which they call the first of metric and the second of projective; metric geometry is based on the notion of distance; two figures are regarded as equivalent when they are “equal” in the … Read More

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The Digital Assembly 2019 is a forum for stakeholders to take stock of the achievements of the Digital Single Market Strategy, draw lessons and to exchange views on the contours of a future digital policy. The event is also a … Read More

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