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principio del buen orden

English translation: well ordering principle

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
Spanish term or phrase:principio del buen orden
English translation:well ordering principle
Entered by: Russell Gillis
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20:52 Apr 8, 2005
Spanish to English translations [PRO]
Tech/Engineering - Mathematics & Statistics / Algebra
Spanish term or phrase: principio del buen orden
Hello,

I am translating someone's transcripts from Mexico (ITAM - Instituto Tecnológico Autónomo de México), and there is one particular part of a course where I can't find an appropriate English equivalent.

Here is the entire paragraph:

"El principio de inducción matemática. Demostraciones mediante inducción matemática. El principio de inducción matemática modificado. ***El principio del buen orden.*** Relación entre ***el principio del buen orden*** y el principio de inducción matemática."

I have done a lot of searching already, so please don't answer unless you have a plausible answer (i.e. "principle of good order" or "good order principle" will not work).

Thanks!
Russell Gillis
Local time: 00:21
well ordering principle
Explanation:
Saludos =:) Espero que sirva!

Well Ordering Principle -- from MathWorld - [ Traduzca esta página ]
... Apostol, TM "The Well-Ordering Principle." §I 4.3 in Calculus, 2nd ed., Vol.
1: One-Variable Calculus, with an Introduction to Linear Algebra. ...
mathworld.wolfram.com/WellOrderingPrinciple.html - 17k - En caché - Páginas similares

The Well Ordering Principle - [ Traduzca esta página ]
Math reference, the well ordering principle. ... The "well ordering principle"
says yes, but it really depends on the axiom of choice. ...
www.mathreference.com/set-card,wop.html - 8k - En caché - Páginas similares

Selected response from:

Leopoldo Gurman
Local time: 03:21
Grading comment
Thank you very much to both answerers. I researched both terms, and found this article:

"An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually exclusive nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.

In Zermelo-Fraenkel set theory (in the form omitting the axiom of choice), the Zorn's lemma, trichotomy law, and the well ordering principle are equivalent to the axiom of choice (Mendelson 1997, p. 275). In contexts sensitive to the axiom of choice, the notation "ZF" is often used to denote Zermelo-Fraenkel without the axiom of choice, while "ZFC" is used if the axiom of choice is included."

So apparently these are two different concepts (although it says they are equivalent).
4 KudoZ points were awarded for this answer



Summary of answers provided
5 +3well ordering principle
Leopoldo Gurman
5Axiom of choicezorp


  

Answers


4 mins   confidence: Answerer confidence 5/5 peer agreement (net): +3
well ordering principle


Explanation:
Saludos =:) Espero que sirva!

Well Ordering Principle -- from MathWorld - [ Traduzca esta página ]
... Apostol, TM "The Well-Ordering Principle." §I 4.3 in Calculus, 2nd ed., Vol.
1: One-Variable Calculus, with an Introduction to Linear Algebra. ...
mathworld.wolfram.com/WellOrderingPrinciple.html - 17k - En caché - Páginas similares

The Well Ordering Principle - [ Traduzca esta página ]
Math reference, the well ordering principle. ... The "well ordering principle"
says yes, but it really depends on the axiom of choice. ...
www.mathreference.com/set-card,wop.html - 8k - En caché - Páginas similares



Leopoldo Gurman
Local time: 03:21
Works in field
Native speaker of: Spanish
PRO pts in category: 8
Grading comment
Thank you very much to both answerers. I researched both terms, and found this article:

"An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually exclusive nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.

In Zermelo-Fraenkel set theory (in the form omitting the axiom of choice), the Zorn's lemma, trichotomy law, and the well ordering principle are equivalent to the axiom of choice (Mendelson 1997, p. 275). In contexts sensitive to the axiom of choice, the notation "ZF" is often used to denote Zermelo-Fraenkel without the axiom of choice, while "ZFC" is used if the axiom of choice is included."

So apparently these are two different concepts (although it says they are equivalent).

Peer comments on this answer (and responses from the answerer)
agree  Andrés Martínez: The Principle of Mathematical Induction and the Well Ordering. Principle.www.math.uwo.ca/~fcass/courses/ Mathematics310a_04/MathInduction.pdf
6 mins
  -> Gracias Urico! =:)

neutral  neilmac: Could be, but sounds a bit odd, like "goodness of fit"
7 mins
  -> It does sound odd. The references are quite sound though. It would be nice to hear from a mathematician. Thanks for your comment neilmac =:)

agree  Gabriela Rodriguez
35 mins
  -> Gracias again, gaby! =:) Buen finde!

agree  PTLtda: i've looked at the definitions in english and spanish, and this is correct.
3 hrs
  -> Gracias Andrew! =:) For your agree and your research!
Login to enter a peer comment (or grade)

4 hrs   confidence: Answerer confidence 5/5
Axiom of choice


Explanation:
In mathematics, the axiom of choice is an axiom of set theory. It was formulated in 1904 by Ernst Zermelo and has remained controversial to this day. It states the following:

Let X be a collection of non-empty sets. Then we can choose a member from each set in that collection.

Stated more formally:

There exists a function f defined on X such that for each set S in X, f(S) is an element of S.

Another formulation of the axiom of choice (AC) states:

Given any set of mutually exclusive non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets



    Reference: http://en.wikipedia.org/wiki/Axiom_of_choice
zorp
Native speaker of: Native in PortuguesePortuguese
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