Help with the notation $(x,t)in mathbb R^n times (0,infty)$

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What is the meaning of $$(x,t)in mathbb R^n times (0,infty)quad ?tag 1label1$$




I guess $x$ is a $n$-vector and $t$ is just a scalar, i.e.
beginalign
x&=(x_1, x_2, dots, x_n)in mathbb R^n tag 2\
t&in (0,infty) tag 3
endalign



Attempt 1:



Does eqref1 mean I have , i.e.
beginalign
(x_1, t), (x_2,t), dots, (x_n,t) tag 4
endalign
I.e. $n$ number of points in $mathbb R^2$ (I guess?).



Attempt 2:



Or does eqref1 mean
beginalign
(x_1, x_2, dots, x_n,t) tag 5
endalign
I.e. just one point. But how many dimensions?




multivariable-calculus elementary-set-theory notation vectors




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  • 2




    Attempt 2 is the correct one. The vector $(x_1, x_2, ldots, x_n, t)$ is $(n+1)$-dimensional.
    – Sobi
    Aug 14 at 10:24











  • I've edited your post to add links pointing to equation (1) for easy reference.
    – GNU Supporter
    Aug 14 at 10:29














up vote
2
down vote

favorite













What is the meaning of $$(x,t)in mathbb R^n times (0,infty)quad ?tag 1label1$$




I guess $x$ is a $n$-vector and $t$ is just a scalar, i.e.
beginalign
x&=(x_1, x_2, dots, x_n)in mathbb R^n tag 2\
t&in (0,infty) tag 3
endalign



Attempt 1:



Does eqref1 mean I have , i.e.
beginalign
(x_1, t), (x_2,t), dots, (x_n,t) tag 4
endalign
I.e. $n$ number of points in $mathbb R^2$ (I guess?).



Attempt 2:



Or does eqref1 mean
beginalign
(x_1, x_2, dots, x_n,t) tag 5
endalign
I.e. just one point. But how many dimensions?




multivariable-calculus elementary-set-theory notation vectors




share|cite|improve this question


















  • 2




    Attempt 2 is the correct one. The vector $(x_1, x_2, ldots, x_n, t)$ is $(n+1)$-dimensional.
    – Sobi
    Aug 14 at 10:24











  • I've edited your post to add links pointing to equation (1) for easy reference.
    – GNU Supporter
    Aug 14 at 10:29












up vote
2
down vote

favorite









up vote
2
down vote

favorite












What is the meaning of $$(x,t)in mathbb R^n times (0,infty)quad ?tag 1label1$$




I guess $x$ is a $n$-vector and $t$ is just a scalar, i.e.
beginalign
x&=(x_1, x_2, dots, x_n)in mathbb R^n tag 2\
t&in (0,infty) tag 3
endalign



Attempt 1:



Does eqref1 mean I have , i.e.
beginalign
(x_1, t), (x_2,t), dots, (x_n,t) tag 4
endalign
I.e. $n$ number of points in $mathbb R^2$ (I guess?).



Attempt 2:



Or does eqref1 mean
beginalign
(x_1, x_2, dots, x_n,t) tag 5
endalign
I.e. just one point. But how many dimensions?




multivariable-calculus elementary-set-theory notation vectors




share|cite|improve this question















What is the meaning of $$(x,t)in mathbb R^n times (0,infty)quad ?tag 1label1$$




I guess $x$ is a $n$-vector and $t$ is just a scalar, i.e.
beginalign
x&=(x_1, x_2, dots, x_n)in mathbb R^n tag 2\
t&in (0,infty) tag 3
endalign



Attempt 1:



Does eqref1 mean I have , i.e.
beginalign
(x_1, t), (x_2,t), dots, (x_n,t) tag 4
endalign
I.e. $n$ number of points in $mathbb R^2$ (I guess?).



Attempt 2:



Or does eqref1 mean
beginalign
(x_1, x_2, dots, x_n,t) tag 5
endalign
I.e. just one point. But how many dimensions?





multivariable-calculus elementary-set-theory notation vectors





share|cite|improve this question













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edited Aug 14 at 10:28









GNU Supporter

11.8k72143




11.8k72143










asked Aug 14 at 10:22









JDoeDoe

7471513




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  • 2




    Attempt 2 is the correct one. The vector $(x_1, x_2, ldots, x_n, t)$ is $(n+1)$-dimensional.
    – Sobi
    Aug 14 at 10:24











  • I've edited your post to add links pointing to equation (1) for easy reference.
    – GNU Supporter
    Aug 14 at 10:29












  • 2




    Attempt 2 is the correct one. The vector $(x_1, x_2, ldots, x_n, t)$ is $(n+1)$-dimensional.
    – Sobi
    Aug 14 at 10:24











  • I've edited your post to add links pointing to equation (1) for easy reference.
    – GNU Supporter
    Aug 14 at 10:29







2




2




Attempt 2 is the correct one. The vector $(x_1, x_2, ldots, x_n, t)$ is $(n+1)$-dimensional.
– Sobi
Aug 14 at 10:24





Attempt 2 is the correct one. The vector $(x_1, x_2, ldots, x_n, t)$ is $(n+1)$-dimensional.
– Sobi
Aug 14 at 10:24













I've edited your post to add links pointing to equation (1) for easy reference.
– GNU Supporter
Aug 14 at 10:29




I've edited your post to add links pointing to equation (1) for easy reference.
– GNU Supporter
Aug 14 at 10:29










1 Answer
1






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5
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It is shorthand for the pair $(x, t)$ with
$x in mathbbR^n, t in (0, infty)$, thus
$$
((x_1, dotsc, x_n), t)
$$
This nested tuple can be mapped to the flat tuple
$$
(x_1, dotsc, x_n, t)
$$
of course.






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    up vote
    5
    down vote













    It is shorthand for the pair $(x, t)$ with
    $x in mathbbR^n, t in (0, infty)$, thus
    $$
    ((x_1, dotsc, x_n), t)
    $$
    This nested tuple can be mapped to the flat tuple
    $$
    (x_1, dotsc, x_n, t)
    $$
    of course.






    share|cite|improve this answer
























      up vote
      5
      down vote













      It is shorthand for the pair $(x, t)$ with
      $x in mathbbR^n, t in (0, infty)$, thus
      $$
      ((x_1, dotsc, x_n), t)
      $$
      This nested tuple can be mapped to the flat tuple
      $$
      (x_1, dotsc, x_n, t)
      $$
      of course.






      share|cite|improve this answer






















        up vote
        5
        down vote










        up vote
        5
        down vote









        It is shorthand for the pair $(x, t)$ with
        $x in mathbbR^n, t in (0, infty)$, thus
        $$
        ((x_1, dotsc, x_n), t)
        $$
        This nested tuple can be mapped to the flat tuple
        $$
        (x_1, dotsc, x_n, t)
        $$
        of course.






        share|cite|improve this answer












        It is shorthand for the pair $(x, t)$ with
        $x in mathbbR^n, t in (0, infty)$, thus
        $$
        ((x_1, dotsc, x_n), t)
        $$
        This nested tuple can be mapped to the flat tuple
        $$
        (x_1, dotsc, x_n, t)
        $$
        of course.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 14 at 10:32









        mvw

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