Writing “a function is integrable provided it is continous” in the form “if $P$ then $Q$”.












2












$begingroup$



I came across the statement



"a function is integrable provided it is continous"



and was asked to rewrite it in the form "If $P$ then $Q$".




I identified from the initial statment that the continous condition of a function is a neccassary one for a function to be integrable, but this is wrong, why is this so?



My answer was "If a function is integrable then it is continous" but this is wrong in the book it says "If a function is continous then that function is integrable"






logic







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    You flip the terms in your answer: $X$ is necessary for $Y$ is equivalent to $Y implies X$, not the other way around.
    $endgroup$
    – platty
    Nov 30 '18 at 3:37












  • $begingroup$
    This seems to be a question about English rather than one about logic.
    $endgroup$
    – Henning Makholm
    Nov 30 '18 at 4:00
















2












$begingroup$



I came across the statement



"a function is integrable provided it is continous"



and was asked to rewrite it in the form "If $P$ then $Q$".




I identified from the initial statment that the continous condition of a function is a neccassary one for a function to be integrable, but this is wrong, why is this so?



My answer was "If a function is integrable then it is continous" but this is wrong in the book it says "If a function is continous then that function is integrable"






logic







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    You flip the terms in your answer: $X$ is necessary for $Y$ is equivalent to $Y implies X$, not the other way around.
    $endgroup$
    – platty
    Nov 30 '18 at 3:37












  • $begingroup$
    This seems to be a question about English rather than one about logic.
    $endgroup$
    – Henning Makholm
    Nov 30 '18 at 4:00














2












2








2





$begingroup$



I came across the statement



"a function is integrable provided it is continous"



and was asked to rewrite it in the form "If $P$ then $Q$".




I identified from the initial statment that the continous condition of a function is a neccassary one for a function to be integrable, but this is wrong, why is this so?



My answer was "If a function is integrable then it is continous" but this is wrong in the book it says "If a function is continous then that function is integrable"






logic







share|cite|improve this question











$endgroup$





I came across the statement



"a function is integrable provided it is continous"



and was asked to rewrite it in the form "If $P$ then $Q$".




I identified from the initial statment that the continous condition of a function is a neccassary one for a function to be integrable, but this is wrong, why is this so?



My answer was "If a function is integrable then it is continous" but this is wrong in the book it says "If a function is continous then that function is integrable"






logic




logic






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 30 '18 at 3:54









Shaun

8,893113681




8,893113681










asked Nov 30 '18 at 3:36









Carlos BaccaCarlos Bacca

180116




180116








  • 1




    $begingroup$
    You flip the terms in your answer: $X$ is necessary for $Y$ is equivalent to $Y implies X$, not the other way around.
    $endgroup$
    – platty
    Nov 30 '18 at 3:37












  • $begingroup$
    This seems to be a question about English rather than one about logic.
    $endgroup$
    – Henning Makholm
    Nov 30 '18 at 4:00














  • 1




    $begingroup$
    You flip the terms in your answer: $X$ is necessary for $Y$ is equivalent to $Y implies X$, not the other way around.
    $endgroup$
    – platty
    Nov 30 '18 at 3:37












  • $begingroup$
    This seems to be a question about English rather than one about logic.
    $endgroup$
    – Henning Makholm
    Nov 30 '18 at 4:00








1




1




$begingroup$
You flip the terms in your answer: $X$ is necessary for $Y$ is equivalent to $Y implies X$, not the other way around.
$endgroup$
– platty
Nov 30 '18 at 3:37






$begingroup$
You flip the terms in your answer: $X$ is necessary for $Y$ is equivalent to $Y implies X$, not the other way around.
$endgroup$
– platty
Nov 30 '18 at 3:37














$begingroup$
This seems to be a question about English rather than one about logic.
$endgroup$
– Henning Makholm
Nov 30 '18 at 4:00




$begingroup$
This seems to be a question about English rather than one about logic.
$endgroup$
– Henning Makholm
Nov 30 '18 at 4:00










3 Answers
3






active

oldest

votes


















4












$begingroup$

To place emphasis, it's




A function is integrable provided it is continous.




In other words, if I provide you with a continuous function, then, according to the statement, you can deduce that that function is integrable.



Thus, given a function, $P$ is "it is continuous" and $Q$ is "it is integrable", using your notation.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
    $endgroup$
    – Carlos Bacca
    Nov 30 '18 at 3:49






  • 2




    $begingroup$
    You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
    $endgroup$
    – Shaun
    Nov 30 '18 at 3:51



















1












$begingroup$


Provided : make available for use , enable/allow.




In mathematics, to "provide" an assumption is to say that it is to be assumed true.Therefore, in the above, you can see that "provided the function is continuous" is asking us to assume that the function is continuous. The conclusion is then that the function is integrable.



In other words, $P implies Q$ is the same as "if $P$ then $Q$" which is the same as "$Q$ is true if $P$ is true" (often just stated as "$Q$ if $P$"). "Provided ____" just means "if _____ is true"(or just, "if _____"). So, $P implies Q$ is the same as "$Q$ is true provided $P$ is true".



Therefore, "a function is integrable provided it is continuous" would translate into the implication $P implies Q$, where $P$ is "the function is continuous" and $Q$ is "the function is integrable".






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    Saying "a function is integrable provided it is continuous" is equivalent to saying "a function is integrable if it is continuous." From there, you just need to switch the order of the statements to end up with "If a function is continuous, then it is integrable."






    share|cite|improve this answer









    $endgroup$













      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      4












      $begingroup$

      To place emphasis, it's




      A function is integrable provided it is continous.




      In other words, if I provide you with a continuous function, then, according to the statement, you can deduce that that function is integrable.



      Thus, given a function, $P$ is "it is continuous" and $Q$ is "it is integrable", using your notation.






      share|cite|improve this answer









      $endgroup$













      • $begingroup$
        Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
        $endgroup$
        – Carlos Bacca
        Nov 30 '18 at 3:49






      • 2




        $begingroup$
        You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
        $endgroup$
        – Shaun
        Nov 30 '18 at 3:51
















      4












      $begingroup$

      To place emphasis, it's




      A function is integrable provided it is continous.




      In other words, if I provide you with a continuous function, then, according to the statement, you can deduce that that function is integrable.



      Thus, given a function, $P$ is "it is continuous" and $Q$ is "it is integrable", using your notation.






      share|cite|improve this answer









      $endgroup$













      • $begingroup$
        Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
        $endgroup$
        – Carlos Bacca
        Nov 30 '18 at 3:49






      • 2




        $begingroup$
        You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
        $endgroup$
        – Shaun
        Nov 30 '18 at 3:51














      4












      4








      4





      $begingroup$

      To place emphasis, it's




      A function is integrable provided it is continous.




      In other words, if I provide you with a continuous function, then, according to the statement, you can deduce that that function is integrable.



      Thus, given a function, $P$ is "it is continuous" and $Q$ is "it is integrable", using your notation.






      share|cite|improve this answer









      $endgroup$



      To place emphasis, it's




      A function is integrable provided it is continous.




      In other words, if I provide you with a continuous function, then, according to the statement, you can deduce that that function is integrable.



      Thus, given a function, $P$ is "it is continuous" and $Q$ is "it is integrable", using your notation.







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      answered Nov 30 '18 at 3:44









      ShaunShaun

      8,893113681




      8,893113681












      • $begingroup$
        Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
        $endgroup$
        – Carlos Bacca
        Nov 30 '18 at 3:49






      • 2




        $begingroup$
        You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
        $endgroup$
        – Shaun
        Nov 30 '18 at 3:51


















      • $begingroup$
        Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
        $endgroup$
        – Carlos Bacca
        Nov 30 '18 at 3:49






      • 2




        $begingroup$
        You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
        $endgroup$
        – Shaun
        Nov 30 '18 at 3:51
















      $begingroup$
      Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
      $endgroup$
      – Carlos Bacca
      Nov 30 '18 at 3:49




      $begingroup$
      Thanks, its just a bit confusing because i think in normal english you could replace the 'provided' with 'only if'
      $endgroup$
      – Carlos Bacca
      Nov 30 '18 at 3:49




      2




      2




      $begingroup$
      You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
      $endgroup$
      – Shaun
      Nov 30 '18 at 3:51




      $begingroup$
      You're welcome, @CarlosBacca. Yeah, it does take some getting used to. The best thing to do is just practice. If you read enough mathematical literature and write enough proofs, it'll become second nature to you.
      $endgroup$
      – Shaun
      Nov 30 '18 at 3:51











      1












      $begingroup$


      Provided : make available for use , enable/allow.




      In mathematics, to "provide" an assumption is to say that it is to be assumed true.Therefore, in the above, you can see that "provided the function is continuous" is asking us to assume that the function is continuous. The conclusion is then that the function is integrable.



      In other words, $P implies Q$ is the same as "if $P$ then $Q$" which is the same as "$Q$ is true if $P$ is true" (often just stated as "$Q$ if $P$"). "Provided ____" just means "if _____ is true"(or just, "if _____"). So, $P implies Q$ is the same as "$Q$ is true provided $P$ is true".



      Therefore, "a function is integrable provided it is continuous" would translate into the implication $P implies Q$, where $P$ is "the function is continuous" and $Q$ is "the function is integrable".






      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$


        Provided : make available for use , enable/allow.




        In mathematics, to "provide" an assumption is to say that it is to be assumed true.Therefore, in the above, you can see that "provided the function is continuous" is asking us to assume that the function is continuous. The conclusion is then that the function is integrable.



        In other words, $P implies Q$ is the same as "if $P$ then $Q$" which is the same as "$Q$ is true if $P$ is true" (often just stated as "$Q$ if $P$"). "Provided ____" just means "if _____ is true"(or just, "if _____"). So, $P implies Q$ is the same as "$Q$ is true provided $P$ is true".



        Therefore, "a function is integrable provided it is continuous" would translate into the implication $P implies Q$, where $P$ is "the function is continuous" and $Q$ is "the function is integrable".






        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$


          Provided : make available for use , enable/allow.




          In mathematics, to "provide" an assumption is to say that it is to be assumed true.Therefore, in the above, you can see that "provided the function is continuous" is asking us to assume that the function is continuous. The conclusion is then that the function is integrable.



          In other words, $P implies Q$ is the same as "if $P$ then $Q$" which is the same as "$Q$ is true if $P$ is true" (often just stated as "$Q$ if $P$"). "Provided ____" just means "if _____ is true"(or just, "if _____"). So, $P implies Q$ is the same as "$Q$ is true provided $P$ is true".



          Therefore, "a function is integrable provided it is continuous" would translate into the implication $P implies Q$, where $P$ is "the function is continuous" and $Q$ is "the function is integrable".






          share|cite|improve this answer









          $endgroup$




          Provided : make available for use , enable/allow.




          In mathematics, to "provide" an assumption is to say that it is to be assumed true.Therefore, in the above, you can see that "provided the function is continuous" is asking us to assume that the function is continuous. The conclusion is then that the function is integrable.



          In other words, $P implies Q$ is the same as "if $P$ then $Q$" which is the same as "$Q$ is true if $P$ is true" (often just stated as "$Q$ if $P$"). "Provided ____" just means "if _____ is true"(or just, "if _____"). So, $P implies Q$ is the same as "$Q$ is true provided $P$ is true".



          Therefore, "a function is integrable provided it is continuous" would translate into the implication $P implies Q$, where $P$ is "the function is continuous" and $Q$ is "the function is integrable".







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 30 '18 at 3:45









          астон вілла олоф мэллбэргастон вілла олоф мэллбэрг

          37.5k33376




          37.5k33376























              0












              $begingroup$

              Saying "a function is integrable provided it is continuous" is equivalent to saying "a function is integrable if it is continuous." From there, you just need to switch the order of the statements to end up with "If a function is continuous, then it is integrable."






              share|cite|improve this answer









              $endgroup$


















                0












                $begingroup$

                Saying "a function is integrable provided it is continuous" is equivalent to saying "a function is integrable if it is continuous." From there, you just need to switch the order of the statements to end up with "If a function is continuous, then it is integrable."






                share|cite|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  Saying "a function is integrable provided it is continuous" is equivalent to saying "a function is integrable if it is continuous." From there, you just need to switch the order of the statements to end up with "If a function is continuous, then it is integrable."






                  share|cite|improve this answer









                  $endgroup$



                  Saying "a function is integrable provided it is continuous" is equivalent to saying "a function is integrable if it is continuous." From there, you just need to switch the order of the statements to end up with "If a function is continuous, then it is integrable."







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Nov 30 '18 at 3:43









                  Robert HowardRobert Howard

                  1,9161822




                  1,9161822






























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