set notation confusion - object t is a member of closed interval set?












0












$begingroup$


I'm reading through an introduction to basic set theory and have encountered the following ..



$tin [a, b] Leftrightarrow a leq t :&: t leq b$



I've been trying to figure the above in combination with the Wikipedia list of mathematical symbols, but I'm still not clear how to read this. I understand the part to the right of the "if and only if ..." double headed arrow, but the bit to the left I'm not sure about.



Simple explanations will be preferred over complex ones.






elementary-set-theory notation







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  • $begingroup$
    Are you sure about $bleqslant t$? It should be $tleqslant b$.
    $endgroup$
    – José Carlos Santos
    Jan 8 at 19:49










  • $begingroup$
    Thanks! I've updated the question.
    $endgroup$
    – Chris Snow
    Jan 8 at 19:51










  • $begingroup$
    '$in$' means belongs to
    $endgroup$
    – Shubham Johri
    Jan 8 at 19:58


















0












$begingroup$


I'm reading through an introduction to basic set theory and have encountered the following ..



$tin [a, b] Leftrightarrow a leq t :&: t leq b$



I've been trying to figure the above in combination with the Wikipedia list of mathematical symbols, but I'm still not clear how to read this. I understand the part to the right of the "if and only if ..." double headed arrow, but the bit to the left I'm not sure about.



Simple explanations will be preferred over complex ones.






elementary-set-theory notation







share|cite|improve this question











$endgroup$












  • $begingroup$
    Are you sure about $bleqslant t$? It should be $tleqslant b$.
    $endgroup$
    – José Carlos Santos
    Jan 8 at 19:49










  • $begingroup$
    Thanks! I've updated the question.
    $endgroup$
    – Chris Snow
    Jan 8 at 19:51










  • $begingroup$
    '$in$' means belongs to
    $endgroup$
    – Shubham Johri
    Jan 8 at 19:58
















0












0








0





$begingroup$


I'm reading through an introduction to basic set theory and have encountered the following ..



$tin [a, b] Leftrightarrow a leq t :&: t leq b$



I've been trying to figure the above in combination with the Wikipedia list of mathematical symbols, but I'm still not clear how to read this. I understand the part to the right of the "if and only if ..." double headed arrow, but the bit to the left I'm not sure about.



Simple explanations will be preferred over complex ones.






elementary-set-theory notation







share|cite|improve this question











$endgroup$




I'm reading through an introduction to basic set theory and have encountered the following ..



$tin [a, b] Leftrightarrow a leq t :&: t leq b$



I've been trying to figure the above in combination with the Wikipedia list of mathematical symbols, but I'm still not clear how to read this. I understand the part to the right of the "if and only if ..." double headed arrow, but the bit to the left I'm not sure about.



Simple explanations will be preferred over complex ones.






elementary-set-theory notation




elementary-set-theory notation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 8 at 19:50







Chris Snow

















asked Jan 8 at 19:45









Chris SnowChris Snow

1738




1738












  • $begingroup$
    Are you sure about $bleqslant t$? It should be $tleqslant b$.
    $endgroup$
    – José Carlos Santos
    Jan 8 at 19:49










  • $begingroup$
    Thanks! I've updated the question.
    $endgroup$
    – Chris Snow
    Jan 8 at 19:51










  • $begingroup$
    '$in$' means belongs to
    $endgroup$
    – Shubham Johri
    Jan 8 at 19:58




















  • $begingroup$
    Are you sure about $bleqslant t$? It should be $tleqslant b$.
    $endgroup$
    – José Carlos Santos
    Jan 8 at 19:49










  • $begingroup$
    Thanks! I've updated the question.
    $endgroup$
    – Chris Snow
    Jan 8 at 19:51










  • $begingroup$
    '$in$' means belongs to
    $endgroup$
    – Shubham Johri
    Jan 8 at 19:58


















$begingroup$
Are you sure about $bleqslant t$? It should be $tleqslant b$.
$endgroup$
– José Carlos Santos
Jan 8 at 19:49




$begingroup$
Are you sure about $bleqslant t$? It should be $tleqslant b$.
$endgroup$
– José Carlos Santos
Jan 8 at 19:49












$begingroup$
Thanks! I've updated the question.
$endgroup$
– Chris Snow
Jan 8 at 19:51




$begingroup$
Thanks! I've updated the question.
$endgroup$
– Chris Snow
Jan 8 at 19:51












$begingroup$
'$in$' means belongs to
$endgroup$
– Shubham Johri
Jan 8 at 19:58






$begingroup$
'$in$' means belongs to
$endgroup$
– Shubham Johri
Jan 8 at 19:58












2 Answers
2






active

oldest

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3












$begingroup$

You read it as: “$t$ belongs to the closed interval $[a,b]$ if and only if $a$ is smaller than or equal to $t$ and $t$ is smaller than or equal to $b$”.






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    $t$ is the variable $t$. It represents supposedly a real number.



    $in$ means "is a member of" a set. The next thing to follow will be a set of real numbers and the statement is that the number represented by $t$ is an element of the set.



    $[a,b]$ is a set of all the real numbers that are between $a$ and $b$ inclusively. Or in other words the set of all real numbers that are both $ge a$ and $le b$.



    So $t in [a,b]$ means $t$ is the variable representation of a real number that is in the set of all real numbers that are greater or equal to $a$ or less than or equal to $b$.



    Note: $t in [a,b]$ is another way of stating $a le t le b$.



    That's the LHS.



    $iff$ means "if and only if". the LHS is true precisely and only when the RHS is true. If $LHS iff RHS$ then we say "LHS" and "RHS" are equivalent as they are, as far as the rules of the universe allows us to accept reality, the exact same thing. You simply can not have one without the other. We often use these for making definitions. A konkle is defined to be a green blickle. So Jim is a konkle if he is a green blickle and if Jim is a green blickle he is a konkle.



    $a$ is a constant real number $a$



    $le$ is less than or equal to.



    $t$ is a variable for some real number



    & is "and"



    $t$ is our variable again and and $le$ is less than or equal to again.



    $b$ is another constant.



    So RHS is $a$ is less than or equal to $t$ and $t$ is less than or equal too $b$.



    So the statement:



    $t in [a,b] iff a le t & tle b$ means:




    The real number $t$ is a real number in the set of all numbers between $a$ and $b$ inclusively if an only if $a$ is less than or equal to $t$ and $t$ is less than or equal to $b$.




    .... which is .... obvious.



    Basically this is simply defining what the notation $t in [a,b]$ means. $t$ is a member of the set $[a,b]$ if and only if $a le t le b$.



    Another way of putting it is $[a,b]$ is defined to be the set of all real numbers so that $a le $ the real number $le b$.






    share|cite|improve this answer









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      2 Answers
      2






      active

      oldest

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      2 Answers
      2






      active

      oldest

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      active

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      active

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      3












      $begingroup$

      You read it as: “$t$ belongs to the closed interval $[a,b]$ if and only if $a$ is smaller than or equal to $t$ and $t$ is smaller than or equal to $b$”.






      share|cite|improve this answer









      $endgroup$


















        3












        $begingroup$

        You read it as: “$t$ belongs to the closed interval $[a,b]$ if and only if $a$ is smaller than or equal to $t$ and $t$ is smaller than or equal to $b$”.






        share|cite|improve this answer









        $endgroup$
















          3












          3








          3





          $begingroup$

          You read it as: “$t$ belongs to the closed interval $[a,b]$ if and only if $a$ is smaller than or equal to $t$ and $t$ is smaller than or equal to $b$”.






          share|cite|improve this answer









          $endgroup$



          You read it as: “$t$ belongs to the closed interval $[a,b]$ if and only if $a$ is smaller than or equal to $t$ and $t$ is smaller than or equal to $b$”.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 8 at 19:53









          José Carlos SantosJosé Carlos Santos

          175k24134243




          175k24134243























              1












              $begingroup$

              $t$ is the variable $t$. It represents supposedly a real number.



              $in$ means "is a member of" a set. The next thing to follow will be a set of real numbers and the statement is that the number represented by $t$ is an element of the set.



              $[a,b]$ is a set of all the real numbers that are between $a$ and $b$ inclusively. Or in other words the set of all real numbers that are both $ge a$ and $le b$.



              So $t in [a,b]$ means $t$ is the variable representation of a real number that is in the set of all real numbers that are greater or equal to $a$ or less than or equal to $b$.



              Note: $t in [a,b]$ is another way of stating $a le t le b$.



              That's the LHS.



              $iff$ means "if and only if". the LHS is true precisely and only when the RHS is true. If $LHS iff RHS$ then we say "LHS" and "RHS" are equivalent as they are, as far as the rules of the universe allows us to accept reality, the exact same thing. You simply can not have one without the other. We often use these for making definitions. A konkle is defined to be a green blickle. So Jim is a konkle if he is a green blickle and if Jim is a green blickle he is a konkle.



              $a$ is a constant real number $a$



              $le$ is less than or equal to.



              $t$ is a variable for some real number



              & is "and"



              $t$ is our variable again and and $le$ is less than or equal to again.



              $b$ is another constant.



              So RHS is $a$ is less than or equal to $t$ and $t$ is less than or equal too $b$.



              So the statement:



              $t in [a,b] iff a le t & tle b$ means:




              The real number $t$ is a real number in the set of all numbers between $a$ and $b$ inclusively if an only if $a$ is less than or equal to $t$ and $t$ is less than or equal to $b$.




              .... which is .... obvious.



              Basically this is simply defining what the notation $t in [a,b]$ means. $t$ is a member of the set $[a,b]$ if and only if $a le t le b$.



              Another way of putting it is $[a,b]$ is defined to be the set of all real numbers so that $a le $ the real number $le b$.






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                $t$ is the variable $t$. It represents supposedly a real number.



                $in$ means "is a member of" a set. The next thing to follow will be a set of real numbers and the statement is that the number represented by $t$ is an element of the set.



                $[a,b]$ is a set of all the real numbers that are between $a$ and $b$ inclusively. Or in other words the set of all real numbers that are both $ge a$ and $le b$.



                So $t in [a,b]$ means $t$ is the variable representation of a real number that is in the set of all real numbers that are greater or equal to $a$ or less than or equal to $b$.



                Note: $t in [a,b]$ is another way of stating $a le t le b$.



                That's the LHS.



                $iff$ means "if and only if". the LHS is true precisely and only when the RHS is true. If $LHS iff RHS$ then we say "LHS" and "RHS" are equivalent as they are, as far as the rules of the universe allows us to accept reality, the exact same thing. You simply can not have one without the other. We often use these for making definitions. A konkle is defined to be a green blickle. So Jim is a konkle if he is a green blickle and if Jim is a green blickle he is a konkle.



                $a$ is a constant real number $a$



                $le$ is less than or equal to.



                $t$ is a variable for some real number



                & is "and"



                $t$ is our variable again and and $le$ is less than or equal to again.



                $b$ is another constant.



                So RHS is $a$ is less than or equal to $t$ and $t$ is less than or equal too $b$.



                So the statement:



                $t in [a,b] iff a le t & tle b$ means:




                The real number $t$ is a real number in the set of all numbers between $a$ and $b$ inclusively if an only if $a$ is less than or equal to $t$ and $t$ is less than or equal to $b$.




                .... which is .... obvious.



                Basically this is simply defining what the notation $t in [a,b]$ means. $t$ is a member of the set $[a,b]$ if and only if $a le t le b$.



                Another way of putting it is $[a,b]$ is defined to be the set of all real numbers so that $a le $ the real number $le b$.






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  $t$ is the variable $t$. It represents supposedly a real number.



                  $in$ means "is a member of" a set. The next thing to follow will be a set of real numbers and the statement is that the number represented by $t$ is an element of the set.



                  $[a,b]$ is a set of all the real numbers that are between $a$ and $b$ inclusively. Or in other words the set of all real numbers that are both $ge a$ and $le b$.



                  So $t in [a,b]$ means $t$ is the variable representation of a real number that is in the set of all real numbers that are greater or equal to $a$ or less than or equal to $b$.



                  Note: $t in [a,b]$ is another way of stating $a le t le b$.



                  That's the LHS.



                  $iff$ means "if and only if". the LHS is true precisely and only when the RHS is true. If $LHS iff RHS$ then we say "LHS" and "RHS" are equivalent as they are, as far as the rules of the universe allows us to accept reality, the exact same thing. You simply can not have one without the other. We often use these for making definitions. A konkle is defined to be a green blickle. So Jim is a konkle if he is a green blickle and if Jim is a green blickle he is a konkle.



                  $a$ is a constant real number $a$



                  $le$ is less than or equal to.



                  $t$ is a variable for some real number



                  & is "and"



                  $t$ is our variable again and and $le$ is less than or equal to again.



                  $b$ is another constant.



                  So RHS is $a$ is less than or equal to $t$ and $t$ is less than or equal too $b$.



                  So the statement:



                  $t in [a,b] iff a le t & tle b$ means:




                  The real number $t$ is a real number in the set of all numbers between $a$ and $b$ inclusively if an only if $a$ is less than or equal to $t$ and $t$ is less than or equal to $b$.




                  .... which is .... obvious.



                  Basically this is simply defining what the notation $t in [a,b]$ means. $t$ is a member of the set $[a,b]$ if and only if $a le t le b$.



                  Another way of putting it is $[a,b]$ is defined to be the set of all real numbers so that $a le $ the real number $le b$.






                  share|cite|improve this answer









                  $endgroup$



                  $t$ is the variable $t$. It represents supposedly a real number.



                  $in$ means "is a member of" a set. The next thing to follow will be a set of real numbers and the statement is that the number represented by $t$ is an element of the set.



                  $[a,b]$ is a set of all the real numbers that are between $a$ and $b$ inclusively. Or in other words the set of all real numbers that are both $ge a$ and $le b$.



                  So $t in [a,b]$ means $t$ is the variable representation of a real number that is in the set of all real numbers that are greater or equal to $a$ or less than or equal to $b$.



                  Note: $t in [a,b]$ is another way of stating $a le t le b$.



                  That's the LHS.



                  $iff$ means "if and only if". the LHS is true precisely and only when the RHS is true. If $LHS iff RHS$ then we say "LHS" and "RHS" are equivalent as they are, as far as the rules of the universe allows us to accept reality, the exact same thing. You simply can not have one without the other. We often use these for making definitions. A konkle is defined to be a green blickle. So Jim is a konkle if he is a green blickle and if Jim is a green blickle he is a konkle.



                  $a$ is a constant real number $a$



                  $le$ is less than or equal to.



                  $t$ is a variable for some real number



                  & is "and"



                  $t$ is our variable again and and $le$ is less than or equal to again.



                  $b$ is another constant.



                  So RHS is $a$ is less than or equal to $t$ and $t$ is less than or equal too $b$.



                  So the statement:



                  $t in [a,b] iff a le t & tle b$ means:




                  The real number $t$ is a real number in the set of all numbers between $a$ and $b$ inclusively if an only if $a$ is less than or equal to $t$ and $t$ is less than or equal to $b$.




                  .... which is .... obvious.



                  Basically this is simply defining what the notation $t in [a,b]$ means. $t$ is a member of the set $[a,b]$ if and only if $a le t le b$.



                  Another way of putting it is $[a,b]$ is defined to be the set of all real numbers so that $a le $ the real number $le b$.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jan 8 at 20:18









                  fleabloodfleablood

                  1




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