"It can now be made clear what is to be understood, in general, by a mathematical structure. The common character of the different concepts designated by this generic name, is that they can be applied to sets of elements whose nature has not been specified; to define a structure, one takes as given one or several relations, into which these elements enter (in the case of groups, this was the relation z = xτy between three arbitrary elements); then one postulates that the given relation, or relations, satisfy certain conditions (which are explicitly stated and which are the axioms of the structure under consideration.) To set up the axiomatic theory of a given structure, amounts to the deduction of the logical consequences of the axioms of the structure, excluding every other hypothesis on the elements under consideration (in particular, every hypotheses as to their own nature)."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/Nicolas_Bourbaki
Revision History
No revisions have been submitted for this quote.
Categories
Related Quotes
"The "structures" are tools for the mathematician; as soon as he has recognized among the elements, which he is studyi…"
"... in a single view, it sweeps over immense domains, now unified by the axiomatic method, but which were formerly in…"
"At the center of our universe are found the great types of structures... they might be called the mother-structures..…"
"From the axiomatic point of view, mathematics appears thus as a storehouse of abstract forms -- the mathematical stru…"
"Nicolas Bourbaki is the nom-de-plume adopted in the 1930s by a group of out standing young French mathematicians who …"
"But in the eyes of contemporary structuralist mathematicians, like the Bourbaki, the Erlanger Program amounts to only…"
"This present art, in which we use those twice five Indian figures, is called algorismus."
"It was not exactly as you say. In practice, the 12 of us never lived at home at the same time, because the family gre…"
"In this respect I recall with much sympathy the writer Virginia Woolf who wrote about this need for private space (A …"
"Hermite was born in 1822, four years before Riemann. Now in his sixties, he had become one of the standard-bearers fo…"