What is the difference of the following two mathematical sentences? (Walter Rudin's Principles of...












0












$begingroup$


I am very poor at English.

But I am reading Walter Rudin's Principles of Mathematical Analysis now.



In the book, I found the following sentence:




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




I cannot understand why "the set $E$" instead of "a set $E$".



What is the difference in meaning between the following two mathematical sentences?



(1)




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




(2)




A point $p$ is a limit point of a set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.







soft-question







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  • 6




    $begingroup$
    There's no difference.
    $endgroup$
    – Chris Custer
    Dec 29 '18 at 4:40






  • 3




    $begingroup$
    No difference really. For the first may be the set $E$ was already introduced so "the" would be used to refer to that specific one.
    $endgroup$
    – Pratyush Sarkar
    Dec 29 '18 at 4:43










  • $begingroup$
    Thank you very much, Chris Custer and Pratyush Sarkar.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07
















0












$begingroup$


I am very poor at English.

But I am reading Walter Rudin's Principles of Mathematical Analysis now.



In the book, I found the following sentence:




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




I cannot understand why "the set $E$" instead of "a set $E$".



What is the difference in meaning between the following two mathematical sentences?



(1)




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




(2)




A point $p$ is a limit point of a set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.







soft-question







share|cite|improve this question









$endgroup$








  • 6




    $begingroup$
    There's no difference.
    $endgroup$
    – Chris Custer
    Dec 29 '18 at 4:40






  • 3




    $begingroup$
    No difference really. For the first may be the set $E$ was already introduced so "the" would be used to refer to that specific one.
    $endgroup$
    – Pratyush Sarkar
    Dec 29 '18 at 4:43










  • $begingroup$
    Thank you very much, Chris Custer and Pratyush Sarkar.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07














0












0








0





$begingroup$


I am very poor at English.

But I am reading Walter Rudin's Principles of Mathematical Analysis now.



In the book, I found the following sentence:




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




I cannot understand why "the set $E$" instead of "a set $E$".



What is the difference in meaning between the following two mathematical sentences?



(1)




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




(2)




A point $p$ is a limit point of a set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.







soft-question







share|cite|improve this question









$endgroup$




I am very poor at English.

But I am reading Walter Rudin's Principles of Mathematical Analysis now.



In the book, I found the following sentence:




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




I cannot understand why "the set $E$" instead of "a set $E$".



What is the difference in meaning between the following two mathematical sentences?



(1)




A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.




(2)




A point $p$ is a limit point of a set $E$ if every neighborhood of $p$ contains a point $q neq p$ such that $q in E$.







soft-question




soft-question






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 29 '18 at 4:36









tchappy hatchappy ha

773412




773412








  • 6




    $begingroup$
    There's no difference.
    $endgroup$
    – Chris Custer
    Dec 29 '18 at 4:40






  • 3




    $begingroup$
    No difference really. For the first may be the set $E$ was already introduced so "the" would be used to refer to that specific one.
    $endgroup$
    – Pratyush Sarkar
    Dec 29 '18 at 4:43










  • $begingroup$
    Thank you very much, Chris Custer and Pratyush Sarkar.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07














  • 6




    $begingroup$
    There's no difference.
    $endgroup$
    – Chris Custer
    Dec 29 '18 at 4:40






  • 3




    $begingroup$
    No difference really. For the first may be the set $E$ was already introduced so "the" would be used to refer to that specific one.
    $endgroup$
    – Pratyush Sarkar
    Dec 29 '18 at 4:43










  • $begingroup$
    Thank you very much, Chris Custer and Pratyush Sarkar.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07








6




6




$begingroup$
There's no difference.
$endgroup$
– Chris Custer
Dec 29 '18 at 4:40




$begingroup$
There's no difference.
$endgroup$
– Chris Custer
Dec 29 '18 at 4:40




3




3




$begingroup$
No difference really. For the first may be the set $E$ was already introduced so "the" would be used to refer to that specific one.
$endgroup$
– Pratyush Sarkar
Dec 29 '18 at 4:43




$begingroup$
No difference really. For the first may be the set $E$ was already introduced so "the" would be used to refer to that specific one.
$endgroup$
– Pratyush Sarkar
Dec 29 '18 at 4:43












$begingroup$
Thank you very much, Chris Custer and Pratyush Sarkar.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07




$begingroup$
Thank you very much, Chris Custer and Pratyush Sarkar.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07










1 Answer
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$begingroup$

There's no fundamental difference; to say "the set $E$" or "a set $E$" are both equally valid, grammatically, and Rudin isn't referring to a special or particular set either. It's just how some people word things sometimes.



While not particularly mathematical, this did remind me of another Stack Exchange question I saw recently. You might find it worth looking at: here ya go






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you very much, Eevee Trainer.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07











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1 Answer
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1 Answer
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active

oldest

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active

oldest

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active

oldest

votes









1












$begingroup$

There's no fundamental difference; to say "the set $E$" or "a set $E$" are both equally valid, grammatically, and Rudin isn't referring to a special or particular set either. It's just how some people word things sometimes.



While not particularly mathematical, this did remind me of another Stack Exchange question I saw recently. You might find it worth looking at: here ya go






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you very much, Eevee Trainer.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07
















1












$begingroup$

There's no fundamental difference; to say "the set $E$" or "a set $E$" are both equally valid, grammatically, and Rudin isn't referring to a special or particular set either. It's just how some people word things sometimes.



While not particularly mathematical, this did remind me of another Stack Exchange question I saw recently. You might find it worth looking at: here ya go






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thank you very much, Eevee Trainer.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07














1












1








1





$begingroup$

There's no fundamental difference; to say "the set $E$" or "a set $E$" are both equally valid, grammatically, and Rudin isn't referring to a special or particular set either. It's just how some people word things sometimes.



While not particularly mathematical, this did remind me of another Stack Exchange question I saw recently. You might find it worth looking at: here ya go






share|cite|improve this answer









$endgroup$



There's no fundamental difference; to say "the set $E$" or "a set $E$" are both equally valid, grammatically, and Rudin isn't referring to a special or particular set either. It's just how some people word things sometimes.



While not particularly mathematical, this did remind me of another Stack Exchange question I saw recently. You might find it worth looking at: here ya go







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 29 '18 at 4:44









Eevee TrainerEevee Trainer

8,32421439




8,32421439












  • $begingroup$
    Thank you very much, Eevee Trainer.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07


















  • $begingroup$
    Thank you very much, Eevee Trainer.
    $endgroup$
    – tchappy ha
    Dec 29 '18 at 5:07
















$begingroup$
Thank you very much, Eevee Trainer.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07




$begingroup$
Thank you very much, Eevee Trainer.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07


















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