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supremo e ínfimo

English translation: supremum and infimum / least upper bound (LUB) and greatest lower bound (GLB)


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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
Spanish term or phrase:supremo e ínfimo
English translation:supremum and infimum / least upper bound (LUB) and greatest lower bound (GLB)
Entered by: Charles Davis
Options:
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21:21 Feb 18, 2011
Spanish to English translations [PRO]
Chemistry; Chem Sci/Eng
Spanish term or phrase: supremo e ínfimo
Se trata del programa de estudios de la materia Análisis Matemático I. Cuando enuncia el contenido del programa, dice lo siguiente:
Números reales. Propiedades Basicas. Representacion sobre la recta. Supremo e ínfimo. Axioma del supremo.
Mi duda es con relación al término"supremo e ínfimo". Es correcto si lo traduzco como "highest and lowest"? Axiom of the highest?
Muchas gracias!
Karina Rodriguez
Local time: 02:15
supremum and infimum
Explanation:
Or as the title of a course perhaps "suprema" and "infima".

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Note added at 21 mins (2011-02-18 21:43:09 GMT)
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"En matemáticas, dado un subconjunto S de un conjunto parcialmente ordenado (P, <), el supremo de S, si existe, es el mínimo elemento de P que es mayor o igual a cada elemento de S."
http://es.wikipedia.org/wiki/Supremo

"In mathematics, given a subset S of a partially ordered set T, the supremum (sup) of S, if it exists, is the least element of T that is greater than or equal to each element of S."
http://en.wikipedia.org/wiki/Supremum

"In mathematics, particularly set theory, the infimum (plural infima) of a subset of some set is the greatest element (not necessarily in the subset) that is less than or equal to all elements of the subset."
http://en.wikipedia.org/wiki/Infimum


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Note added at 15 hrs (2011-02-19 13:20:48 GMT)
--------------------------------------------------

As a course or module title, "Supremum and Infimum" is certainly found. For example, at Oxford:

"Topic 1: Sets and Sequences
Sets and sequences: open, closed, bounded, compact, and convex sets, supremum and infimum, convergence, continuity."

"Supremum and Infimum questions
Please could some help me with the following questions finding the sup, inf, max and min. Thank you."
http://www.thestudentroom.co.uk/showthread.php?t=699123

"Exam Information for Math 141
"For the exam, make sure that you know
The precise statement of basic definitions (this is not an exhaustive list): supremum, infimum, upper- and lower-bounds, accumulation points, etc.; what it means for a sequence to converge, the limit of a function, etc."
http://www.math.sunysb.edu/~scott/mat141.fall10/Exams/

"Mathematics 225
4) Properties of Continuous Functions (2 weeks)
Supremum and infimum, Bolzano-Weierstrass property, Cauchy sequences, intermediate value theorem, uniform continuity."
http://www.columbiacollege.ca/ko/content/mathematics-225-ana...

http://malroy.econ.ox.ac.uk/ccw/Maths.shtml

Selected response from:

Charles Davis
Local time: 07:15
Grading comment
Muchas gracias!
4 KudoZ points were awarded for this answer



Summary of answers provided
4 +2supremum and infimumCharles Davis


  

Answers


18 mins   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +2
supremum and infimum


Explanation:
Or as the title of a course perhaps "suprema" and "infima".

--------------------------------------------------
Note added at 21 mins (2011-02-18 21:43:09 GMT)
--------------------------------------------------

"En matemáticas, dado un subconjunto S de un conjunto parcialmente ordenado (P, <), el supremo de S, si existe, es el mínimo elemento de P que es mayor o igual a cada elemento de S."
http://es.wikipedia.org/wiki/Supremo

"In mathematics, given a subset S of a partially ordered set T, the supremum (sup) of S, if it exists, is the least element of T that is greater than or equal to each element of S."
http://en.wikipedia.org/wiki/Supremum

"In mathematics, particularly set theory, the infimum (plural infima) of a subset of some set is the greatest element (not necessarily in the subset) that is less than or equal to all elements of the subset."
http://en.wikipedia.org/wiki/Infimum


--------------------------------------------------
Note added at 15 hrs (2011-02-19 13:20:48 GMT)
--------------------------------------------------

As a course or module title, "Supremum and Infimum" is certainly found. For example, at Oxford:

"Topic 1: Sets and Sequences
Sets and sequences: open, closed, bounded, compact, and convex sets, supremum and infimum, convergence, continuity."

"Supremum and Infimum questions
Please could some help me with the following questions finding the sup, inf, max and min. Thank you."
http://www.thestudentroom.co.uk/showthread.php?t=699123

"Exam Information for Math 141
"For the exam, make sure that you know
The precise statement of basic definitions (this is not an exhaustive list): supremum, infimum, upper- and lower-bounds, accumulation points, etc.; what it means for a sequence to converge, the limit of a function, etc."
http://www.math.sunysb.edu/~scott/mat141.fall10/Exams/

"Mathematics 225
4) Properties of Continuous Functions (2 weeks)
Supremum and infimum, Bolzano-Weierstrass property, Cauchy sequences, intermediate value theorem, uniform continuity."
http://www.columbiacollege.ca/ko/content/mathematics-225-ana...

http://malroy.econ.ox.ac.uk/ccw/Maths.shtml



Charles Davis
Local time: 07:15
Native speaker of: Native in EnglishEnglish
PRO pts in category: 16
Grading comment
Muchas gracias!

Peer comments on this answer (and responses from the answerer)
agree  Cecilia Rey
7 mins
  -> Gracias, Cecilia

agree  coolbrowne: Generally, English-speaking mathematicians would say "least upper bound" and "greatest lower bound", often shortened to LUB and GLB. However, as the title of a section or chapter "Supremum and Infimum" works better.
19 hrs
  -> This is handsome of you, coolbrowne. I didn't intend that you should withdraw! But many thanks for your agreement, and for the information.
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Changes made by editors
Feb 23, 2011 - Changes made by Charles Davis:
Created KOG entryKudoZ term => KOG term


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