A Quote by Emile Borel
Any argument where one supposes an arbitrary choice to be made an uncountably infinite number of times ...[is] outside the domain of mathematics.
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The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.
I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.
Far be it from us to doubt that all number is known to Him 'Whose understanding is infinite' (Ps. 147:5). The infinity of number, though there be no numbering of infinite numbers, is yet not incomprehensible by Him Whose understanding is infinite. And thus, if everything which is comprehended is defined or made finite by the comprehension of him who knows it, then all infinity is in some ineffable way made finite to God, for it is comprehensible by His knowledge.
Russia has made its choice in favor of democracy. Fourteen years ago, independently, without any pressure from outside, it made that decision in the interests of itself and interests of its people - of its citizens. This is our final choice, and we have no way back. There can be no return to what we used to have before.
While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics.
I refuse to let something as insignificant as a size or number on a scale determine how I feel about myself. I am grateful for my body, my health, and the life that I have, and no arbitrary number should have any impact on that.
It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.
There is no longer a single idea explaining everything, but an infinite number of essences giving a meaning to an infinite number of objects. The world comes to a stop, but also lights up.
Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.
Creativity is any act, idea, or product that changes an existing domain, or that transforms an existing domain into a new one What counts is whether the novelty he or she produces is accepted for inclusion in the domain.
One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
The problem, of course, was that turning into a monster was the brighter of my two choices. Choice Number 1: I turn into a vampyre, which equals a monster in just about any human’s mind. Choice Number 2: My body rejects the Change and I die. Forever. So the good news is that I wouldn’t have to take the geometry test tomorrow.
Name me the final number, the highest, the greatest. But that's absurd! If the number of numbers is infinite, how can there be a final number? Then how can you speak of a final revolution? There is no final one. Revolutions are infinite.
I recognize the amount of time that it takes as a director. I made the choice to stop taking roles outside of L.A. because I didn't want to miss any of my child's life.
A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.
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