Definitions for well-ordered
well-or·dered

Princeton's WordNetRate this definition:0.0 / 0 votes

1. well-orderedadjective

   ordered well

   "well-ordered work habits"

WiktionaryRate this definition:0.0 / 0 votes

1. well-orderedadjective

   Having a precise arrangement.

2. well-orderedadjective

   Having a well-order.

WikipediaRate this definition:0.0 / 0 votes

1. well-ordered

   In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the well-order relation is then called a well-ordered set. In some academic articles and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering. Every non-empty well-ordered set has a least element. Every element s of a well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater than s. There may be elements besides the least element which have no predecessor (see § Natural numbers below for an example). A well-ordered set S contains for every subset T with an upper bound a least upper bound, namely the least element of the subset of all upper bounds of T in S. If ≤ is a non-strict well ordering, then < is a strict well ordering. A relation is a strict well ordering if and only if it is a well-founded strict total order. The distinction between strict and non-strict well orders is often ignored since they are easily interconvertible. Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set. The well-ordering theorem, which is equivalent to the axiom of choice, states that every set can be well ordered. If a set is well ordered (or even if it merely admits a well-founded relation), the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the set. The observation that the natural numbers are well ordered by the usual less-than relation is commonly called the well-ordering principle (for natural numbers).

ChatGPTRate this definition:0.0 / 0 votes

1. well-ordered

   A set is well-ordered if it has a relation that is a well-ordering. A relation is a well-ordering if it orders the set such that every non-empty subset has a least element. In other words, for any selection of elements within the set, there is always at least one element that is smaller than all the others according to that relation. It implies that every non-empty subset of it has a smallest element under the ordering.

How to pronounce well-ordered?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say well-ordered in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of well-ordered in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of well-ordered in Pythagorean Numerology is: 4

Examples of well-ordered in a Sentence

1. Sir Thomas Browne:

   Sure there is music even in the beauty, and the silent note which Cupid strikes, far sweeter than the sound of an instrument. For there is music wherever there is harmony, order and proportion; and thus far we may maintain the music of the spheres; for those well ordered motions, and regular paces, though they give no sound unto the ear, yet to the understanding they strike a note most full of harmony.

2. Lucius Annaeus Seneca:

   The primary sign of a well-ordered mind is a man's ability to remain in one place and linger in his own company.

3. Marcel Neeleman:

   Most galaxies that we find early in the universe look like train wrecks because they underwent consistent and often' violent' merging, these hot mergers make Milky Way difficult to form well-ordered, cold rotating disks like we observe in our present universe.

4. Marcus Aurelius Antoninus:

   By a tranquil mind I mean nothing else than a mind well ordered.

5. Thomas Aquinas:

   Well-ordered self-love is right and natural.

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=well-ordered
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Well-Ordered
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Well-Ordered
4. ^ ChatGPT
   https://chat.openai.com