$x = 3$ in $Bbb Z_5$ equivalent to saying $x equiv 3 pmod 5$?












2












$begingroup$


I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?






linear-algebra







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  • 1




    $begingroup$
    Yes. ${}{}{}{}$
    $endgroup$
    – YiFan
    Dec 10 '18 at 1:25










  • $begingroup$
    @WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
    $endgroup$
    – Bill Dubuque
    Dec 10 '18 at 3:11
















2












$begingroup$


I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?






linear-algebra







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Yes. ${}{}{}{}$
    $endgroup$
    – YiFan
    Dec 10 '18 at 1:25










  • $begingroup$
    @WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
    $endgroup$
    – Bill Dubuque
    Dec 10 '18 at 3:11














2












2








2


1



$begingroup$


I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?






linear-algebra







share|cite|improve this question











$endgroup$




I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?






linear-algebra




linear-algebra






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 10 '18 at 5:47









Moo

5,60131020




5,60131020










asked Dec 10 '18 at 1:01









mingming

3415




3415








  • 1




    $begingroup$
    Yes. ${}{}{}{}$
    $endgroup$
    – YiFan
    Dec 10 '18 at 1:25










  • $begingroup$
    @WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
    $endgroup$
    – Bill Dubuque
    Dec 10 '18 at 3:11














  • 1




    $begingroup$
    Yes. ${}{}{}{}$
    $endgroup$
    – YiFan
    Dec 10 '18 at 1:25










  • $begingroup$
    @WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
    $endgroup$
    – Bill Dubuque
    Dec 10 '18 at 3:11








1




1




$begingroup$
Yes. ${}{}{}{}$
$endgroup$
– YiFan
Dec 10 '18 at 1:25




$begingroup$
Yes. ${}{}{}{}$
$endgroup$
– YiFan
Dec 10 '18 at 1:25












$begingroup$
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
$endgroup$
– Bill Dubuque
Dec 10 '18 at 3:11




$begingroup$
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
$endgroup$
– Bill Dubuque
Dec 10 '18 at 3:11










1 Answer
1






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2












$begingroup$

If one accepts that



$Bbb Z / (5) equiv Bbb Z_5, tag 1$



then it is evident that



$x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$



means that



$x in 3 + (5), tag 3$



that is,



$x - 3 = 5n, ; n in Bbb Z, tag 4$



i.e.,



$x equiv 3 pmod 5. tag 5$



If I were grading the test I would accept either notation as correct.






share|cite|improve this answer











$endgroup$













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    2












    $begingroup$

    If one accepts that



    $Bbb Z / (5) equiv Bbb Z_5, tag 1$



    then it is evident that



    $x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$



    means that



    $x in 3 + (5), tag 3$



    that is,



    $x - 3 = 5n, ; n in Bbb Z, tag 4$



    i.e.,



    $x equiv 3 pmod 5. tag 5$



    If I were grading the test I would accept either notation as correct.






    share|cite|improve this answer











    $endgroup$


















      2












      $begingroup$

      If one accepts that



      $Bbb Z / (5) equiv Bbb Z_5, tag 1$



      then it is evident that



      $x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$



      means that



      $x in 3 + (5), tag 3$



      that is,



      $x - 3 = 5n, ; n in Bbb Z, tag 4$



      i.e.,



      $x equiv 3 pmod 5. tag 5$



      If I were grading the test I would accept either notation as correct.






      share|cite|improve this answer











      $endgroup$
















        2












        2








        2





        $begingroup$

        If one accepts that



        $Bbb Z / (5) equiv Bbb Z_5, tag 1$



        then it is evident that



        $x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$



        means that



        $x in 3 + (5), tag 3$



        that is,



        $x - 3 = 5n, ; n in Bbb Z, tag 4$



        i.e.,



        $x equiv 3 pmod 5. tag 5$



        If I were grading the test I would accept either notation as correct.






        share|cite|improve this answer











        $endgroup$



        If one accepts that



        $Bbb Z / (5) equiv Bbb Z_5, tag 1$



        then it is evident that



        $x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$



        means that



        $x in 3 + (5), tag 3$



        that is,



        $x - 3 = 5n, ; n in Bbb Z, tag 4$



        i.e.,



        $x equiv 3 pmod 5. tag 5$



        If I were grading the test I would accept either notation as correct.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Dec 10 '18 at 3:12









        Bill Dubuque

        210k29192640




        210k29192640










        answered Dec 10 '18 at 1:22









        Robert LewisRobert Lewis

        45.9k23066




        45.9k23066






























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