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September 28th, 2008, 07:45 PM   #1
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terms "non-increasing" or "non-decreasing"

My question may look silly for the mathematicians guys but I really wonder why the terms "non-increasing" or "non-decreasing" are used to describe the nature of sequences in standard "Real Analysis" texts instead of simple "increasing" or "decreasing" terms.
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September 29th, 2008, 02:06 AM   #2
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Re: terms "non-increasing" or "non-decreasing"

In Anglo-saxon 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 Anglo-saxon terminology, this same sequence will be said to be non-decreasing. The same consideration applies to the terminology "nonnegative".
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September 29th, 2008, 07:06 AM   #3
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Re: terms "non-increasing" or "non-decreasing"

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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