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In my math book, everywhere the author has used "non-ascending" instead of descending and "non-descending" instead of ascending.
I was wondering if there is some special meaning or use associated with it?
Because the way I see it is that it just increases the number of words and wastes ink.

Git Gud
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Siddharth Thevaril
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    I was, on more than one occasion, struck by confusion because of this terminology. I still instinctively read 'non-increasing' as 'it's false that it is increasing'. It's really unnecessary to use this terminology as we could (and order theorists do) use 'increasing' for the non-strict inequality and 'strictly increasing' for the strict inequality. Since most of the time we're interested in the non-strict inequality, the typing and space advantages are enormous. – Git Gud Jan 28 '15 at 12:41
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    The terms "non-assending" and "non-decending" allow the output to remain flat for some (or all) time for all time. For example $f(x) = 3$ is both "non-assending" and "non-decending" and is neither "assending" nor "decending" for all $x$. – Warren Hill Jan 28 '15 at 12:46

1 Answers1

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The sequence 2, 2, 2, 3, 4 is not increasing, but it's non-decreasing.

The sequence 2, 3, 4, 5, 6 is both increasing and non-decreasing.

Compare the difference between "less than" and "not greater than."

(I have never seen the words ascending/descending used in this context but I imagine it's the same).

hunter
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    Put differently, "non-decreasing" means "increasing but not necessarily strictly increasing" and "increasing" means "strictly increasing", at least for authors using such terminology. – PhoemueX Jan 28 '15 at 12:37