What is the difference of the following two mathematical sentences? (Walter Rudin's Principles of...
$begingroup$
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
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
$endgroup$
add a comment |
$begingroup$
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
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
$endgroup$
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
add a comment |
$begingroup$
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
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
$endgroup$
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
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
asked Dec 29 '18 at 4:36
tchappy hatchappy ha
731412
731412
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
$begingroup$
Thank you very much, Eevee Trainer.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3055530%2fwhat-is-the-difference-of-the-following-two-mathematical-sentences-walter-rudi%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
$begingroup$
Thank you very much, Eevee Trainer.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07
add a comment |
$begingroup$
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
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
$begingroup$
Thank you very much, Eevee Trainer.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07
add a comment |
$begingroup$
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
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
$endgroup$
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
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
answered Dec 29 '18 at 4:44
Eevee TrainerEevee Trainer
6,56811237
6,56811237
$begingroup$
Thank you very much, Eevee Trainer.
$endgroup$
– tchappy ha
Dec 29 '18 at 5:07
add a comment |
$begingroup$
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
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3055530%2fwhat-is-the-difference-of-the-following-two-mathematical-sentences-walter-rudi%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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