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searching for Well-ordering principle 5 found (20 total)

Controversy over Cantor's theory (2,978 words) [view diff] exact match in snippet view article find links to article

proof used his well-ordering principle "every set can be well-ordered", which he called a "law of thought". The well-ordering principle is equivalent to

Jerry L. Bona (372 words) [view diff] exact match in snippet view article find links to article

Applied Mathematics. The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma? This is a

Transfer principle (2,686 words) [view diff] exact match in snippet view article find links to article

*R. Consequently the set of all infinitesimals is external. The well-ordering principle implies every nonempty internal subset of *N has a smallest member

Georg Cantor (10,164 words) [view diff] exact match in snippet view article find links to article

larger ordinals to add to it. In 1883, Cantor also introduced the well-ordering principle "every set can be well-ordered" and stated that it is a "law of

Zorn's lemma (4,668 words) [view diff] exact match in snippet view article find links to article

attributed to Jerry Bona: "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" Zorn's lemma