Dedekind cut
A Dedekind cut in an ordered field is a partition of it, (A, B), such that A is closed downwards (meaning that whenever a is in A and x ≤ a, then x is in A as well), B is closed upwards and A has no maximum.The Dedekind cut is named after Richard Dedekind, who invented this construction in order to represent the real numbers as Dedekind cuts of the rational numbers. A typical Dedekind cut of the rational numbers is given by A = { a in Q : a2 < 2 }, B = { b in Q : b2 ≥ 2 }. This cut represents the real number √ 2 in Dedekind's construction.
- this is a stub article
See also:
Cressida
dreadful cheer, and oft his hues mue [change];" she likes "all
manner, and his gentleness;" so that, however she may have
shall not pull it out this nexte week." Pandarus, striking the iron
she strenuously declines, for fear of scandal, and because it is all
love.html">love.html">love.html">love him unknown of all, "and guerdon [reward] him with
while Troilus writes daily letters with increasing love, he
the brother of Troilus, he tells him that Cressida is in danger of
Deiphobus gladly complies, promises the protection of Hector
Meantime Pandarus instructs Troilus to go to the house of
and keep his chamber next day. "Lo," says the crafty promoter
thee at thy tristre [tryst <33>] close, and I shall well the deer
comes to dinner.html">dinner; and at table, Helen, Pandarus, and others,
that she has the love of such a knight. After dinner they speak
protection and aid; and Pandarus suggests that, since Troilus is
Deiphobus alone accompany Pandarus to Troilus' chamber;
weal, which Hector has sent for his opinion; Helen and
the chamber, by a stair, into the garden; while Pandarus goes
still with Troilus, brings Cressida to her lover.html">lover. The Second
be merciful and kind to her lover, that hath for her such pain;
whispering without, and wondering what he shall say for this
God! what shall he say?"
To the Third Book is prefixed a beautiful invocation of Venus,
Adornen all the thirde heaven fair!
Pleasance of love, O goodly debonair,* *lovely and gracious*
O very* cause of heal** and of gladness, *true.
On
wordlookup.net
All is still licensed under the GNU FDL.
It uses material from the wikipedia.
|
|