Ring, field, injection, surjection, bijection,

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SUMMARY

The discussion centers on the origins and meanings of mathematical terms such as "ring," "field," "injection," "surjection," and "bijection." Participants explore the etymology of these terms, noting that "field" is derived from the German word "körper," while "ring" likely comes from the French "anneau." The conversation emphasizes the connection between these mathematical structures and their real-world associations, particularly in the context of natural numbers and their tangible representations.

PREREQUISITES
  • Understanding of basic mathematical concepts such as sets and functions.
  • Familiarity with terminology in abstract algebra, specifically "rings" and "fields."
  • Knowledge of mathematical mappings, including injections, surjections, and bijections.
  • Basic grasp of etymology related to mathematical terminology.
NEXT STEPS
  • Research the historical development of abstract algebra concepts, focusing on "rings" and "fields."
  • Explore the properties and applications of injections, surjections, and bijections in mathematics.
  • Study the relationship between natural numbers and their representations in various mathematical contexts.
  • Investigate the influence of language on mathematical terminology and its implications for understanding.
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Mathematicians, educators, and students interested in the foundations of abstract algebra and the linguistic roots of mathematical terminology.

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Ring, field, injection, surjection, bijection, jet, bundle.
Does anybody know who first introduced those terms and when and why those people called these matimatical structures so. I mean not the definitions but the properties of real things which can be accosiated with those mathematical structures terms.
For example, 'nutural number' is number which can be associate with the real things in the nuture, e.g. 1,2,3... Number 0 is not nutural, because nobody see zero thing, and the negative number too.
 
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field seems to be a translation from the german of korper, and ring is pesumably also a transl;ation of something like anneau from french, or a german version.

the various jections are french transliterations.
 

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