A Quote by Bertrand Russell

The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.

Bertrand Russell

Quote Topics

Axiom Choice Finite Number Infinite Necessary Number Select Set Shoes Socks

Quote Author

Bertrand Russell
British - Celebrity
May 18, 1872 - February 2, 1970

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.

Albert Camus

To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.

Bertrand Russell

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.

Yevgeny Zamyatin

Without doubt, matter is unlimited in extent, and, in this sense, infinite; and the forces of Nature mould it into an innumerable number of worlds. Would it be at all astonishing if, from the universal dice-box, out of an innumberable number of throws, there should be thrown out one world infinitely perfect? Nay, does not the calculus of probabilities prove to us that one such world out of an infinite number, must be produced of necessity?

William Batchelder Greene

To photograph is often compared to an act of redemption - to select from an infinite number of choices that which is to be remembered.

John Divola

This is a work of fiction. Still, given an infinite number of possible worlds, it must be true on one of them. And if a story set in an infinite number of possible worlds is true in one of them, then it must be true in all of them. So maybe, it's not as fictional as we think.

Neil Gaiman

What we, thanks to Jung, call "synchronicity" (coincidence on steroids), Buddhists have long known as "the interpenetration of realities." Whether it's a natural law of sorts or simply evidence of mathematical inevitability (an infinite number of monkeys locked up with an infinite number of typewriters eventually producing 'Hamlet,' not to mention 'Tarzan of the Apes'), it seems to be as real as it is eerie.

Tom Robbins

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.

Saint Augustine

All things were together, infinite both in number and in smallness; for the small too was infinite.

Anaxagoras

Now, legal plunder can be committed in an infinite number of ways. Thus we have an infinite number of plans for organizing it: tariffs, protection, benefits, subsidies, encouragements, progressive taxation, public schools, guaranteed jobs, guaranteed profits, minimum wages, a right to relief, a right to the tools of labor, free credit, and so on, and so on.

Frederic Bastiat

There are infinite worlds both like and unlike this world of ours. For the atoms being infinite in number... are borne on far out into space.

Epicurus

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.

Douglas Adams

Any argument where one supposes an arbitrary choice to be made an uncountably infinite number of times ...[is] outside the domain of mathematics.

Emile Borel

Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers: the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy (entropy).

Yevgeny Zamyatin

I can count the number of great Cabernets I made at Beaulieu only by taking off my socks and shoes, but I can count the number of great Pinot Noirs on one hand with change left over.