Tom/Yaakov,
Getting back to the slightly related field of specification
of standard protocols, the term "monotonically increasing" is used
in many cases because that is all that really needs to be said.
This is because the intent in the specification is to allow
implementations to detect a "roll-over" or "restart" event by the
simple process of checking to see if a new value is less than a
prior value.
Since this is the test that the implementations actually
need to be able to perform in many cases, it is often sufficient
to say exactly "monotonically increasing" and not necessary to
say more than that.
--
Eric
--> -----Original Message-----
--> From: Yaakov Stein [mailto:yaakov_s(_at_)rad(_dot_)com]
--> Sent: Monday, February 20, 2006 11:12 AM
--> To: Tom.Petch
--> Cc: ietf
--> Subject: RE: 'monotonic increasing'
-->
-->
-->
--> > But just to be clear, if you saw a reference to
--> 'monotonic increasing'
--> in an American journal,
--> > say of applied mathematics, would you be sure you
--> understood what was
--> meant?
-->
-->
--> That would depend on the subject matter.
--> If the article was on real analysis (where the domain is
--> nondenumerable),
--> then it would most probably mean >=.
--> If the article's subject matter was "concrete mathematics" (i.e.
--> discrete values)
--> then "increasing" would probably mean > and only
--> "nondecreasing" would
--> mean >=.
-->
--> So in the case you raise, monotonic increasing would
--> usually be strictly
--> interpreted as x_n > x_n-1,
--> and if you want to include the case where the sequence
--> doesn't actually
--> increase
--> you should say "nondecreasing" .
-->
--> However, since the Godel failure of Principia Mathematica
--> even mathematicians have lost faith in consistent definitions :>
-->
--> Y(J)S
-->
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