Axiom Of Choice Quotes & Sayings

That is, for a mathematical Platonist, what the C.H. proofs really show is that set theory needs to find a better set of core axioms than classical ZFS, or at least it will need to add some further postulates that are-like the Axiom of Choice-both "self-evident" and Consistent with classical axioms. If you're interested, Godel's own personal view was that the Continuum Hypothesis is false, that there are actually a whole (Infinity Symbol) of Zeno-type (Infinity Symbol)s nested between (Aleph0) and c, and that sooner or later a principle would be found that proved this. As of now no such principle's ever been found. Godel and Cantor both died in confinement, bequeathing a world with no finite circumference. One that spins, now, in a new kind of all-formal Void. Mathematics continues to get out of bed. — David Foster Wallace

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

The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions. — Alonzo Church

My morality, the morality of reason, is contained in a single axiom: existence exists - and in a single choice: to live. — Ayn Rand

However, Nick acted as much as possible under the circumstances, and that was rectifying - it brought with it enjoyment and a working faith. He had not gone counter to the axiom that in a case of doubt one was to hold off; for that applied to choice, and he had not at present the slightest pretension to choosing. He knew he was lifted along, that what he was doing was not first-rate, that nothing was settled by it and that if there was essentially a problem in his life it would only grow tougher with keeping. But if doing one's sum to-morrow instead of to-day does not make the sum easier it at least makes to-day so. — Henry James

It's a very old axiom, but do you believe the end can justify the means? When there's no choice left? — James Dashner

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