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monotonic    
单调; 单调的; 单调性

单调; 单调的; 单调性

monotonic
单调

monotonic
adj 1: of a sequence or function; consistently increasing and
never decreasing or consistently decreasing and never
increasing in value [synonym: {monotonic}, {monotone}] [ant:
{nonmonotonic}]
2: sounded or spoken in a tone unvarying in pitch; "the owl's
faint monotonous hooting" [synonym: {flat}, {monotone},
{monotonic}, {monotonous}]

Monotonic \Mon`o*ton"ic\, Monotonical \Mon`o*ton"ic*al\, a.
1. Of, pertaining to, or uttered in, a monotone; monotonous.
"Monotonical declamation." --Chesterfield.
[1913 Webster]

2. (Math.) Always increasing or always decreasing, as the
value of the independent variable increases; -- of a
function.
[PJC]

In {domain theory}, a function f : D -> C is monotonic (or
monotone) if

for all x,y in D, x <= y => f(x) <= f(y).

("<=" is written in {LaTeX} as {\sqsubseteq}).

(1994-11-24)


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  • analysis - How can I prove the monotonicity of a function . . .
    Always depends on context: if you are expected to use the derivative, use the derivative At very beginning of an analysis course, the derivative and its properties have not yet been introduced, so one would not want to use it In a calculus course, a derivaive calculation would be expected, so it is safest to do it
  • general topology - Strictly Convex and Strictly Monotonic Preferences . . .
    0 Here is an attempt to make up for my ugly mistake on the strict convexity of Leontieff preferences ;) If I read you right, the guess you want to check is whether for complete, transitive and continuous preferences, strict convexity implies that any monotonic preference relation is also strictly monotonic





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