Why non-increasing is decreasing?












0












$begingroup$


As far as I know, by definition, non-decreasing means increasing and non-increasing means decreasing. My general question is: why some people use non-increasing and non-decreasing?



In fact, it raises some confusing to me. For example, the sequence




$1,2,3,4$




is increasing and thus the sequence




$4,1,2,3$




is non-increasing. So, based on the definition, it is decreasing, but it is not.






definition







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$endgroup$








  • 3




    $begingroup$
    What you think of as nonincreasing isn't what I think of as non-increasing.
    $endgroup$
    – Lord Shark the Unknown
    Dec 19 '18 at 15:21








  • 2




    $begingroup$
    "non-increasing means decreasing" NO : $0,0,0,ldots$ is non-increasing but not decreasing.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 15:22








  • 2




    $begingroup$
    "nonincreasing" $neq$ "not increasing"
    $endgroup$
    – rschwieb
    Dec 19 '18 at 15:24
















0












$begingroup$


As far as I know, by definition, non-decreasing means increasing and non-increasing means decreasing. My general question is: why some people use non-increasing and non-decreasing?



In fact, it raises some confusing to me. For example, the sequence




$1,2,3,4$




is increasing and thus the sequence




$4,1,2,3$




is non-increasing. So, based on the definition, it is decreasing, but it is not.






definition







share|cite|improve this question









$endgroup$








  • 3




    $begingroup$
    What you think of as nonincreasing isn't what I think of as non-increasing.
    $endgroup$
    – Lord Shark the Unknown
    Dec 19 '18 at 15:21








  • 2




    $begingroup$
    "non-increasing means decreasing" NO : $0,0,0,ldots$ is non-increasing but not decreasing.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 15:22








  • 2




    $begingroup$
    "nonincreasing" $neq$ "not increasing"
    $endgroup$
    – rschwieb
    Dec 19 '18 at 15:24














0












0








0





$begingroup$


As far as I know, by definition, non-decreasing means increasing and non-increasing means decreasing. My general question is: why some people use non-increasing and non-decreasing?



In fact, it raises some confusing to me. For example, the sequence




$1,2,3,4$




is increasing and thus the sequence




$4,1,2,3$




is non-increasing. So, based on the definition, it is decreasing, but it is not.






definition







share|cite|improve this question









$endgroup$




As far as I know, by definition, non-decreasing means increasing and non-increasing means decreasing. My general question is: why some people use non-increasing and non-decreasing?



In fact, it raises some confusing to me. For example, the sequence




$1,2,3,4$




is increasing and thus the sequence




$4,1,2,3$




is non-increasing. So, based on the definition, it is decreasing, but it is not.






definition




definition






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 19 '18 at 15:17









zdmzdm

1856




1856








  • 3




    $begingroup$
    What you think of as nonincreasing isn't what I think of as non-increasing.
    $endgroup$
    – Lord Shark the Unknown
    Dec 19 '18 at 15:21








  • 2




    $begingroup$
    "non-increasing means decreasing" NO : $0,0,0,ldots$ is non-increasing but not decreasing.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 15:22








  • 2




    $begingroup$
    "nonincreasing" $neq$ "not increasing"
    $endgroup$
    – rschwieb
    Dec 19 '18 at 15:24














  • 3




    $begingroup$
    What you think of as nonincreasing isn't what I think of as non-increasing.
    $endgroup$
    – Lord Shark the Unknown
    Dec 19 '18 at 15:21








  • 2




    $begingroup$
    "non-increasing means decreasing" NO : $0,0,0,ldots$ is non-increasing but not decreasing.
    $endgroup$
    – Mauro ALLEGRANZA
    Dec 19 '18 at 15:22








  • 2




    $begingroup$
    "nonincreasing" $neq$ "not increasing"
    $endgroup$
    – rschwieb
    Dec 19 '18 at 15:24








3




3




$begingroup$
What you think of as nonincreasing isn't what I think of as non-increasing.
$endgroup$
– Lord Shark the Unknown
Dec 19 '18 at 15:21






$begingroup$
What you think of as nonincreasing isn't what I think of as non-increasing.
$endgroup$
– Lord Shark the Unknown
Dec 19 '18 at 15:21






2




2




$begingroup$
"non-increasing means decreasing" NO : $0,0,0,ldots$ is non-increasing but not decreasing.
$endgroup$
– Mauro ALLEGRANZA
Dec 19 '18 at 15:22






$begingroup$
"non-increasing means decreasing" NO : $0,0,0,ldots$ is non-increasing but not decreasing.
$endgroup$
– Mauro ALLEGRANZA
Dec 19 '18 at 15:22






2




2




$begingroup$
"nonincreasing" $neq$ "not increasing"
$endgroup$
– rschwieb
Dec 19 '18 at 15:24




$begingroup$
"nonincreasing" $neq$ "not increasing"
$endgroup$
– rschwieb
Dec 19 '18 at 15:24










3 Answers
3






active

oldest

votes


















3












$begingroup$

This is a bit of confusing terminology.



"Non-increasing," unfortunately, does not mean "not increasing" - it means "never increasing." So, for example, the sequence $$3,3,2,1$$ is non-increasing - $3not<3, 3not<2, 2not<1$. The definition is similar for non-decreasing. (Note in particular that non-increasing does not imply decreasing, as the above example shows.)



The sequence $$4,1,2,3$$ has both increases ($2$ to $3$) and decreases ($4$ to $1$); so it is - awkwardly - not increasing, not decreasing, not non-increasing, and not non-decreasing.



Ugh!






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    My understanding is that a non-increasing sequence is different than a decreasing one in the sense that decreasing one "decreases every time" and non-increasing "doesn't increase at all" So the example you gave wouldn't be non increasing as it increases from 1 to 2 and 2 to 3.






    share|cite|improve this answer









    $endgroup$





















      0












      $begingroup$

      There are three conditions of change to the next event. Increasing, decreasing and remaining constant. Negative to these three states are non-increasing, non-decreasing and not remaining constant, i.e, varying.
      So they are not mutually exclusive.






      share|cite|improve this answer









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        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        3












        $begingroup$

        This is a bit of confusing terminology.



        "Non-increasing," unfortunately, does not mean "not increasing" - it means "never increasing." So, for example, the sequence $$3,3,2,1$$ is non-increasing - $3not<3, 3not<2, 2not<1$. The definition is similar for non-decreasing. (Note in particular that non-increasing does not imply decreasing, as the above example shows.)



        The sequence $$4,1,2,3$$ has both increases ($2$ to $3$) and decreases ($4$ to $1$); so it is - awkwardly - not increasing, not decreasing, not non-increasing, and not non-decreasing.



        Ugh!






        share|cite|improve this answer









        $endgroup$


















          3












          $begingroup$

          This is a bit of confusing terminology.



          "Non-increasing," unfortunately, does not mean "not increasing" - it means "never increasing." So, for example, the sequence $$3,3,2,1$$ is non-increasing - $3not<3, 3not<2, 2not<1$. The definition is similar for non-decreasing. (Note in particular that non-increasing does not imply decreasing, as the above example shows.)



          The sequence $$4,1,2,3$$ has both increases ($2$ to $3$) and decreases ($4$ to $1$); so it is - awkwardly - not increasing, not decreasing, not non-increasing, and not non-decreasing.



          Ugh!






          share|cite|improve this answer









          $endgroup$
















            3












            3








            3





            $begingroup$

            This is a bit of confusing terminology.



            "Non-increasing," unfortunately, does not mean "not increasing" - it means "never increasing." So, for example, the sequence $$3,3,2,1$$ is non-increasing - $3not<3, 3not<2, 2not<1$. The definition is similar for non-decreasing. (Note in particular that non-increasing does not imply decreasing, as the above example shows.)



            The sequence $$4,1,2,3$$ has both increases ($2$ to $3$) and decreases ($4$ to $1$); so it is - awkwardly - not increasing, not decreasing, not non-increasing, and not non-decreasing.



            Ugh!






            share|cite|improve this answer









            $endgroup$



            This is a bit of confusing terminology.



            "Non-increasing," unfortunately, does not mean "not increasing" - it means "never increasing." So, for example, the sequence $$3,3,2,1$$ is non-increasing - $3not<3, 3not<2, 2not<1$. The definition is similar for non-decreasing. (Note in particular that non-increasing does not imply decreasing, as the above example shows.)



            The sequence $$4,1,2,3$$ has both increases ($2$ to $3$) and decreases ($4$ to $1$); so it is - awkwardly - not increasing, not decreasing, not non-increasing, and not non-decreasing.



            Ugh!







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Dec 19 '18 at 15:23









            Noah SchweberNoah Schweber

            125k10150288




            125k10150288























                1












                $begingroup$

                My understanding is that a non-increasing sequence is different than a decreasing one in the sense that decreasing one "decreases every time" and non-increasing "doesn't increase at all" So the example you gave wouldn't be non increasing as it increases from 1 to 2 and 2 to 3.






                share|cite|improve this answer









                $endgroup$


















                  1












                  $begingroup$

                  My understanding is that a non-increasing sequence is different than a decreasing one in the sense that decreasing one "decreases every time" and non-increasing "doesn't increase at all" So the example you gave wouldn't be non increasing as it increases from 1 to 2 and 2 to 3.






                  share|cite|improve this answer









                  $endgroup$
















                    1












                    1








                    1





                    $begingroup$

                    My understanding is that a non-increasing sequence is different than a decreasing one in the sense that decreasing one "decreases every time" and non-increasing "doesn't increase at all" So the example you gave wouldn't be non increasing as it increases from 1 to 2 and 2 to 3.






                    share|cite|improve this answer









                    $endgroup$



                    My understanding is that a non-increasing sequence is different than a decreasing one in the sense that decreasing one "decreases every time" and non-increasing "doesn't increase at all" So the example you gave wouldn't be non increasing as it increases from 1 to 2 and 2 to 3.







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Dec 19 '18 at 15:23









                    OfyaOfya

                    5198




                    5198























                        0












                        $begingroup$

                        There are three conditions of change to the next event. Increasing, decreasing and remaining constant. Negative to these three states are non-increasing, non-decreasing and not remaining constant, i.e, varying.
                        So they are not mutually exclusive.






                        share|cite|improve this answer









                        $endgroup$


















                          0












                          $begingroup$

                          There are three conditions of change to the next event. Increasing, decreasing and remaining constant. Negative to these three states are non-increasing, non-decreasing and not remaining constant, i.e, varying.
                          So they are not mutually exclusive.






                          share|cite|improve this answer









                          $endgroup$
















                            0












                            0








                            0





                            $begingroup$

                            There are three conditions of change to the next event. Increasing, decreasing and remaining constant. Negative to these three states are non-increasing, non-decreasing and not remaining constant, i.e, varying.
                            So they are not mutually exclusive.






                            share|cite|improve this answer









                            $endgroup$



                            There are three conditions of change to the next event. Increasing, decreasing and remaining constant. Negative to these three states are non-increasing, non-decreasing and not remaining constant, i.e, varying.
                            So they are not mutually exclusive.







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered Dec 19 '18 at 15:25









                            NarasimhamNarasimham

                            20.8k62158




                            20.8k62158






























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