Construction Of The Real Numbers
In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that these axioms are categorical, in the sense that there is a model for the axioms, and any two such models are isomorphic. Any one of these models must be explicitly constructed, and most of these models are built using the basic properties of the rational number system as an ordered field.
Read more about Construction Of The Real Numbers: Synthetic Approach, Explicit Constructions of Models
Famous quotes containing the words construction of the, construction of, construction, real and/or numbers:
“No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)
“No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)
“There’s no art
To find the mind’s construction in the face:
He was a gentleman on whom I built
An absolute trust.”
—William Shakespeare (1564–1616)
“Avarice, the spur of industry, is so obstinate a passion, and works its way through so many real dangers and difficulties, that it is not likely to be scared by an imaginary danger, which is so small that it scarcely admits of calculation.”
—David Hume (1711–1776)
“The forward Youth that would appear
Must now forsake his Muses dear,
Nor in the Shadows sing
His Numbers languishing.”
—Andrew Marvell (1621–1678)