Notation for element of an ordered tuple?

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When $X$ is a set, we can write:




for all $xin X$ ...




But say that $X=(a, b, c, ... ,n)$. I.e. an ordered tuple.



Is it standard notation to still say the following?




for all $xin X$...




It might be confusing because if you interpret it as a sentence in ZFC, then you're not quantifying over the thing you want (you're including the sets representing the order). But how would we write down to quantify over just the elements of the tuple?




notation




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    up vote
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    down vote

    favorite












    When $X$ is a set, we can write:




    for all $xin X$ ...




    But say that $X=(a, b, c, ... ,n)$. I.e. an ordered tuple.



    Is it standard notation to still say the following?




    for all $xin X$...




    It might be confusing because if you interpret it as a sentence in ZFC, then you're not quantifying over the thing you want (you're including the sets representing the order). But how would we write down to quantify over just the elements of the tuple?




    notation




    share|cite|improve this question





















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      When $X$ is a set, we can write:




      for all $xin X$ ...




      But say that $X=(a, b, c, ... ,n)$. I.e. an ordered tuple.



      Is it standard notation to still say the following?




      for all $xin X$...




      It might be confusing because if you interpret it as a sentence in ZFC, then you're not quantifying over the thing you want (you're including the sets representing the order). But how would we write down to quantify over just the elements of the tuple?




      notation




      share|cite|improve this question











      When $X$ is a set, we can write:




      for all $xin X$ ...




      But say that $X=(a, b, c, ... ,n)$. I.e. an ordered tuple.



      Is it standard notation to still say the following?




      for all $xin X$...




      It might be confusing because if you interpret it as a sentence in ZFC, then you're not quantifying over the thing you want (you're including the sets representing the order). But how would we write down to quantify over just the elements of the tuple?





      notation





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      share|cite|improve this question




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      Programmer2134

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          I've seen it written as you wrote it, numerous times. Sometimes conciseness yields better clarity than perfect rigour.



          An alternative is to write the elements of the $t-$uple in an "indexed" form such as $a_1,dots,a_t$, and then quantify over the range of indices ("$forall i$ ... $a_i$ ...").






          share|cite|improve this answer





















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            up vote
            1
            down vote













            I've seen it written as you wrote it, numerous times. Sometimes conciseness yields better clarity than perfect rigour.



            An alternative is to write the elements of the $t-$uple in an "indexed" form such as $a_1,dots,a_t$, and then quantify over the range of indices ("$forall i$ ... $a_i$ ...").






            share|cite|improve this answer

























              up vote
              1
              down vote













              I've seen it written as you wrote it, numerous times. Sometimes conciseness yields better clarity than perfect rigour.



              An alternative is to write the elements of the $t-$uple in an "indexed" form such as $a_1,dots,a_t$, and then quantify over the range of indices ("$forall i$ ... $a_i$ ...").






              share|cite|improve this answer























                up vote
                1
                down vote










                up vote
                1
                down vote









                I've seen it written as you wrote it, numerous times. Sometimes conciseness yields better clarity than perfect rigour.



                An alternative is to write the elements of the $t-$uple in an "indexed" form such as $a_1,dots,a_t$, and then quantify over the range of indices ("$forall i$ ... $a_i$ ...").






                share|cite|improve this answer













                I've seen it written as you wrote it, numerous times. Sometimes conciseness yields better clarity than perfect rigour.



                An alternative is to write the elements of the $t-$uple in an "indexed" form such as $a_1,dots,a_t$, and then quantify over the range of indices ("$forall i$ ... $a_i$ ...").







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered yesterday









                Anonymous

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