phrase "well-ordering principle" is sometimes taken to be synonymous with the "well-ordering theorem", according to which every set can be well-ordered. On...

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

well-ordering theorem to be a "fundamental principle of thought". However, it is considered difficult or even impossible to visualize a well-ordering...

with the induction principle uniquely model the natural numbers. Replacing the induction principle with the well-ordering principle allows for more exotic...

the well-ordering principle. There are other interesting special cases of well-founded induction. When the well-founded relation is the usual ordering on...

induction is equivalent to the well-ordering principle, structural induction is also equivalent to a well-ordering principle. If the set of all structures...

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 thought". Cantor...

In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set X {\displaystyle X} is a quasi-ordering of X {\displaystyle X} for which...

ultimately a contradiction. It is a method which relies on the well-ordering principle, and is often used to show that a given equation, such as a Diophantine...

appropriate setting for the hyperreal transfer principle is the world of internal entities. Thus, the well-ordering property of the natural numbers by transfer...

thought". The well-ordering principle is equivalent to the axiom of choice. Around 1895, Cantor began to regard the well-ordering principle as a theorem...

the ordering principle, OP, and is a weakening of the well-ordering theorem. However, there are models of set theory in which the ordering principle holds...

positive integers, it has a minimum element d = as + bt, by the well-ordering principle. To prove that d is the greatest common divisor of a and b, it...

(in ZF) to three main results: Hausdorff maximal principle Axiom of choice Well-ordering theorem. A well-known joke alluding to this equivalency (which...

{\displaystyle q} and r {\displaystyle r} . Other proofs use the well-ordering principle (i.e., the assertion that every non-empty set of non-negative integers...

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...

Here, for any given computable number x , {\displaystyle x,} the well ordering principle provides that there is a minimal element in S {\displaystyle S}...

has the same cardinality as some ordinal; this statement is the well-ordering principle. It is however possible to discuss the relative cardinality of...

Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's...

The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is...

observes the mediocrity principle, the anthropic principle, the principle of relativity and the cosmological principle. Other well-known principles include...

The Pareto principle (also known as the 80/20 rule, the law of the vital few and the principle of factor sparsity) states that for many outcomes, roughly...

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose...

index finite total orders or well orders with order type ω by natural numbers in a fashion which respects the ordering (either starting with zero or...

well-ordering A well-ordering is a well founded relation, usually also assumed to be a total order well-ordering principle that the positive integers are well-ordered...

1016/0168-0072(91)90022-E. MR 1129778. Kruskal, J. B. (May 1960). "Well-Quasi-Ordering, The Tree Theorem, and Vazsonyi's Conjecture" (PDF). Transactions...

contained in some total order. Stochastic dominance – Partial order between random variables Strict weak ordering – strict partial order "<" in which the relation...

circular ordering (Mosher 1996, p. 109). Some authors call such an ordering a total cyclic order (Isli & Cohn 1998, p. 643), a complete cyclic order (Novák...

Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing...

problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle of parsimony...