Notation convention for ${1,ldots,n}$












4












$begingroup$


Is there any convention for a notational shorthand for the set ${1,ldots,n}$ (defined as ${kinmathbb{N} mid k le n}$), where $ninmathbb{N}$, that the majority of mathematicians are familiar with?



I find that in some cases in which these sets appear often in the same expression, which can reduce readability, or at least aesthetic cleanness; using some sort of abbreviation would alleviate that.






notation







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$endgroup$








  • 3




    $begingroup$
    In combinatorics it is sometimes written as $[n]$.
    $endgroup$
    – Mark
    Jan 7 at 19:48






  • 2




    $begingroup$
    In combinatorial settings $[n]={1,2,ldots ,n}$ is commonly used.
    $endgroup$
    – Anurag A
    Jan 7 at 19:49










  • $begingroup$
    Sometimes, $overline{1,n}$ is used.
    $endgroup$
    – Litho
    Jan 7 at 20:04
















4












$begingroup$


Is there any convention for a notational shorthand for the set ${1,ldots,n}$ (defined as ${kinmathbb{N} mid k le n}$), where $ninmathbb{N}$, that the majority of mathematicians are familiar with?



I find that in some cases in which these sets appear often in the same expression, which can reduce readability, or at least aesthetic cleanness; using some sort of abbreviation would alleviate that.






notation







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    In combinatorics it is sometimes written as $[n]$.
    $endgroup$
    – Mark
    Jan 7 at 19:48






  • 2




    $begingroup$
    In combinatorial settings $[n]={1,2,ldots ,n}$ is commonly used.
    $endgroup$
    – Anurag A
    Jan 7 at 19:49










  • $begingroup$
    Sometimes, $overline{1,n}$ is used.
    $endgroup$
    – Litho
    Jan 7 at 20:04














4












4








4





$begingroup$


Is there any convention for a notational shorthand for the set ${1,ldots,n}$ (defined as ${kinmathbb{N} mid k le n}$), where $ninmathbb{N}$, that the majority of mathematicians are familiar with?



I find that in some cases in which these sets appear often in the same expression, which can reduce readability, or at least aesthetic cleanness; using some sort of abbreviation would alleviate that.






notation







share|cite|improve this question











$endgroup$




Is there any convention for a notational shorthand for the set ${1,ldots,n}$ (defined as ${kinmathbb{N} mid k le n}$), where $ninmathbb{N}$, that the majority of mathematicians are familiar with?



I find that in some cases in which these sets appear often in the same expression, which can reduce readability, or at least aesthetic cleanness; using some sort of abbreviation would alleviate that.






notation




notation






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share|cite|improve this question













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edited Jan 7 at 19:51







Anakhand

















asked Jan 7 at 19:47









AnakhandAnakhand

269114




269114








  • 3




    $begingroup$
    In combinatorics it is sometimes written as $[n]$.
    $endgroup$
    – Mark
    Jan 7 at 19:48






  • 2




    $begingroup$
    In combinatorial settings $[n]={1,2,ldots ,n}$ is commonly used.
    $endgroup$
    – Anurag A
    Jan 7 at 19:49










  • $begingroup$
    Sometimes, $overline{1,n}$ is used.
    $endgroup$
    – Litho
    Jan 7 at 20:04














  • 3




    $begingroup$
    In combinatorics it is sometimes written as $[n]$.
    $endgroup$
    – Mark
    Jan 7 at 19:48






  • 2




    $begingroup$
    In combinatorial settings $[n]={1,2,ldots ,n}$ is commonly used.
    $endgroup$
    – Anurag A
    Jan 7 at 19:49










  • $begingroup$
    Sometimes, $overline{1,n}$ is used.
    $endgroup$
    – Litho
    Jan 7 at 20:04








3




3




$begingroup$
In combinatorics it is sometimes written as $[n]$.
$endgroup$
– Mark
Jan 7 at 19:48




$begingroup$
In combinatorics it is sometimes written as $[n]$.
$endgroup$
– Mark
Jan 7 at 19:48




2




2




$begingroup$
In combinatorial settings $[n]={1,2,ldots ,n}$ is commonly used.
$endgroup$
– Anurag A
Jan 7 at 19:49




$begingroup$
In combinatorial settings $[n]={1,2,ldots ,n}$ is commonly used.
$endgroup$
– Anurag A
Jan 7 at 19:49












$begingroup$
Sometimes, $overline{1,n}$ is used.
$endgroup$
– Litho
Jan 7 at 20:04




$begingroup$
Sometimes, $overline{1,n}$ is used.
$endgroup$
– Litho
Jan 7 at 20:04










3 Answers
3






active

oldest

votes


















4












$begingroup$

I don't know how popular this is but I've seen the convention:
$$[n]equiv{1,2,3,4,ldots n} $$



See for example:
http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf






share|cite|improve this answer









$endgroup$





















    3












    $begingroup$

    It depends on the context, but a couple of equivalent formulations I've seen:




    • You could say ${k}_{k=1}^n$. I saw this often when considering sets of data points, like below, but I see no reason the notation couldn't extrapolate to any set.


    $${(x_1,y_1) ; , ; (x_2,y_2) ; , ; ... ; , ; (x_n,y_n)} = {(x_i,y_i)}_{i=1}^n$$




    • In combinatorics, apparently $[n]$ can be used to represent ${1,...,n}$ as touched on in the comments and by Archimedesprinciple.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
      $endgroup$
      – user150203
      Jan 8 at 4:40





















    3












    $begingroup$

    In homotopy theory, both $[n]$ and $mathbf{n}$ are common and, to a lesser extent, $underline{n}$. None of this matters too much, as long as you define your choice of notation clearly in your writing.






    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









      4












      $begingroup$

      I don't know how popular this is but I've seen the convention:
      $$[n]equiv{1,2,3,4,ldots n} $$



      See for example:
      http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf






      share|cite|improve this answer









      $endgroup$


















        4












        $begingroup$

        I don't know how popular this is but I've seen the convention:
        $$[n]equiv{1,2,3,4,ldots n} $$



        See for example:
        http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf






        share|cite|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          I don't know how popular this is but I've seen the convention:
          $$[n]equiv{1,2,3,4,ldots n} $$



          See for example:
          http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf






          share|cite|improve this answer









          $endgroup$



          I don't know how popular this is but I've seen the convention:
          $$[n]equiv{1,2,3,4,ldots n} $$



          See for example:
          http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 7 at 19:50









          ArchimedesprincipleArchimedesprinciple

          34418




          34418























              3












              $begingroup$

              It depends on the context, but a couple of equivalent formulations I've seen:




              • You could say ${k}_{k=1}^n$. I saw this often when considering sets of data points, like below, but I see no reason the notation couldn't extrapolate to any set.


              $${(x_1,y_1) ; , ; (x_2,y_2) ; , ; ... ; , ; (x_n,y_n)} = {(x_i,y_i)}_{i=1}^n$$




              • In combinatorics, apparently $[n]$ can be used to represent ${1,...,n}$ as touched on in the comments and by Archimedesprinciple.






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
                $endgroup$
                – user150203
                Jan 8 at 4:40


















              3












              $begingroup$

              It depends on the context, but a couple of equivalent formulations I've seen:




              • You could say ${k}_{k=1}^n$. I saw this often when considering sets of data points, like below, but I see no reason the notation couldn't extrapolate to any set.


              $${(x_1,y_1) ; , ; (x_2,y_2) ; , ; ... ; , ; (x_n,y_n)} = {(x_i,y_i)}_{i=1}^n$$




              • In combinatorics, apparently $[n]$ can be used to represent ${1,...,n}$ as touched on in the comments and by Archimedesprinciple.






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
                $endgroup$
                – user150203
                Jan 8 at 4:40
















              3












              3








              3





              $begingroup$

              It depends on the context, but a couple of equivalent formulations I've seen:




              • You could say ${k}_{k=1}^n$. I saw this often when considering sets of data points, like below, but I see no reason the notation couldn't extrapolate to any set.


              $${(x_1,y_1) ; , ; (x_2,y_2) ; , ; ... ; , ; (x_n,y_n)} = {(x_i,y_i)}_{i=1}^n$$




              • In combinatorics, apparently $[n]$ can be used to represent ${1,...,n}$ as touched on in the comments and by Archimedesprinciple.






              share|cite|improve this answer









              $endgroup$



              It depends on the context, but a couple of equivalent formulations I've seen:




              • You could say ${k}_{k=1}^n$. I saw this often when considering sets of data points, like below, but I see no reason the notation couldn't extrapolate to any set.


              $${(x_1,y_1) ; , ; (x_2,y_2) ; , ; ... ; , ; (x_n,y_n)} = {(x_i,y_i)}_{i=1}^n$$




              • In combinatorics, apparently $[n]$ can be used to represent ${1,...,n}$ as touched on in the comments and by Archimedesprinciple.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Jan 7 at 19:53









              Eevee TrainerEevee Trainer

              10.5k31842




              10.5k31842












              • $begingroup$
                In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
                $endgroup$
                – user150203
                Jan 8 at 4:40




















              • $begingroup$
                In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
                $endgroup$
                – user150203
                Jan 8 at 4:40


















              $begingroup$
              In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
              $endgroup$
              – user150203
              Jan 8 at 4:40






              $begingroup$
              In general the notation $left{ f(k) right}_{k = 1}^{n}$ is used to denote a Sequence rather than a Set per sae. There is no absolute way of defining a set but conventional analysis texts tend to use the notation that you have used.
              $endgroup$
              – user150203
              Jan 8 at 4:40













              3












              $begingroup$

              In homotopy theory, both $[n]$ and $mathbf{n}$ are common and, to a lesser extent, $underline{n}$. None of this matters too much, as long as you define your choice of notation clearly in your writing.






              share|cite|improve this answer









              $endgroup$


















                3












                $begingroup$

                In homotopy theory, both $[n]$ and $mathbf{n}$ are common and, to a lesser extent, $underline{n}$. None of this matters too much, as long as you define your choice of notation clearly in your writing.






                share|cite|improve this answer









                $endgroup$
















                  3












                  3








                  3





                  $begingroup$

                  In homotopy theory, both $[n]$ and $mathbf{n}$ are common and, to a lesser extent, $underline{n}$. None of this matters too much, as long as you define your choice of notation clearly in your writing.






                  share|cite|improve this answer









                  $endgroup$



                  In homotopy theory, both $[n]$ and $mathbf{n}$ are common and, to a lesser extent, $underline{n}$. None of this matters too much, as long as you define your choice of notation clearly in your writing.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jan 7 at 20:01









                  RandallRandall

                  10.7k11431




                  10.7k11431






























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