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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! 
  well ordering principle  Explanation: Saludos =:) Espero que sirva!
Well Ordering Principle  from MathWorld  [ Traduzca esta página ]
... Apostol, TM "The WellOrdering Principle." §I 4.3 in Calculus, 2nd ed., Vol.
1: OneVariable 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/setcard,wop.html  8k  En caché  Páginas similares

 Selected response from: Leopoldo Gurman Local time: 15:04
 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 ZermeloFraenkel 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 ZermeloFraenkel 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 
 
Discussion entries: 0 

Automatic update in 00:

4 mins confidence: peer agreement (net): +3 well ordering principle
Explanation: Saludos =:) Espero que sirva!
Well Ordering Principle  from MathWorld  [ Traduzca esta página ]
... Apostol, TM "The WellOrdering Principle." §I 4.3 in Calculus, 2nd ed., Vol.
1: OneVariable 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/setcard,wop.html  8k  En caché  Páginas similares
 Leopoldo Gurman Local time: 15:04 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 ZermeloFraenkel 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 ZermeloFraenkel 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). 

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4 hrs confidence: 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 nonempty 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 nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets
Reference: http://en.wikipedia.org/wiki/Axiom_of_choice
 zorp Native speaker of: Portuguese

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