What does it mean if you take the zero vector in the hyperplane separation theorem?
0
$begingroup$
If you have two disjoint sets V and W, which are compact and convex, then by the separation theorem there exists a vector u such that uv< uw.
However what does it mean if you take u=0?
separation-axioms
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
$endgroup$
add a comment |
0
$begingroup$
If you have two disjoint sets V and W, which are compact and convex, then by the separation theorem there exists a vector u such that uv< uw.
However what does it mean if you take u=0?
separation-axioms
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
$endgroup$
1
$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35
$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37
$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03
add a comment |
0
0
0
$begingroup$
If you have two disjoint sets V and W, which are compact and convex, then by the separation theorem there exists a vector u such that uv< uw.
However what does it mean if you take u=0?
separation-axioms
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
$endgroup$
If you have two disjoint sets V and W, which are compact and convex, then by the separation theorem there exists a vector u such that uv< uw.
However what does it mean if you take u=0?
separation-axioms
separation-axioms
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
asked Jan 15 at 20:32
Ronny LeleuRonny Leleu
11
11
1
$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35
$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37
$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03
add a comment |
1
$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35
$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37
$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03
1
1
$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35
$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35
$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37
$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37
$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03
$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03
add a comment |
0
active
oldest
votes
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
});
}
});
draft saved
draft discarded
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%2f3074933%2fwhat-does-it-mean-if-you-take-the-zero-vector-in-the-hyperplane-separation-theor%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3074933%2fwhat-does-it-mean-if-you-take-the-zero-vector-in-the-hyperplane-separation-theor%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
1
$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35
$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37
$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03