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September 28th, 2008, 08:45 PM  #1 
Newbie Joined: Sep 2008 Posts: 3 Thanks: 0  terms "nonincreasing" or "nondecreasing"
My question may look silly for the mathematicians guys but I really wonder why the terms "nonincreasing" or "nondecreasing" are used to describe the nature of sequences in standard "Real Analysis" texts instead of simple "increasing" or "decreasing" terms.

September 29th, 2008, 03:06 AM  #2 
Site Founder Joined: Nov 2006 From: France Posts: 824 Thanks: 7  Re: terms "nonincreasing" or "nondecreasing"
In Anglosaxon countries, the terms "increasing" and "decreasing" convey a strict meaning: thus, the sequence 1,2,3,4 is increasing, but the sequence 1,2,3,3 is not. However, in some Latin countries (such as France, and under the impulse of Bourbaki), the latter sequence is said to be increasing. According to the Anglosaxon terminology, this same sequence will be said to be nondecreasing. The same consideration applies to the terminology "nonnegative".

September 29th, 2008, 08:06 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: terms "nonincreasing" or "nondecreasing"
Some authors use "increasing" to mean "strictly increasing" (1, 2, 3, but not 1, 1, 3), while others use it to mean "nondecreasing" (1, 2, 3 as well as 1, 1, 3).


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