Every subset equal to original set?Is the void set (∅) a proper subset of every set?Set theory: difference...
Source for Cremation Specifically Not Jewish
What happened to QGIS 2.x LTR?
Six real numbers so that product of any five is the sixth one
Make me a metasequence
What is this waxed root vegetable?
Difference between 'stomach' and 'uterus'
Don't know what I’m looking for regarding removable HDDs?
Did Amazon pay $0 in taxes last year?
How to substitute values from a list into a function?
Can we carry rice to Japan?
Can a space-faring robot still function over a billion years?
Borrowing Characters
I encountered my boss during an on-site interview at another company. Should I bring it up when seeing him next time?
Is there a frame of reference in which I was born before I was conceived?
If a set is open, does that imply that it has no boundary points?
Is it possible to make a clamp function shorter than a ternary in JS?
Levi-Civita symbol: 3D matrix
Canadian citizen, on US no-fly list. What can I do in order to be allowed on flights which go through US airspace?
What are the issues with an additional (limited) concentration slot instead of Bladesong?
Test pad's ESD protection
What's the values for the Freq_Interval column in MSDB.dbo.SysSchedules when Freq_Type is weekly and more than one day is selected in the schedule?
Pure Functions: Does "No Side Effects" Imply "Always Same Output, Given Same Input"?
For a 1-action spell, do I need to take a turn to ready the spell before I can cast it, or can I cast it immediately?
If nine coins are tossed, what is the probability that the number of heads is even?
Every subset equal to original set?
Is the void set (∅) a proper subset of every set?Set theory: difference between belong/contained and includes/subset?Proving every infinite set is a subset of some denumerable set and vice versaIf the empty set is a subset of every set, why isn't ${emptyset,{a}}={{a}}$?What is the reason behind calling $emptyset$ improper subset of any non-empty set.?Can subset of a countable set be uncountable?Set Theory Subset QuestionIs every empty set equal?Why a set that is subset/equal to infinite set isn't infinite? (by definition)Why the empty set is a subset of every set?
$begingroup$
Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.
elementary-set-theory
asked 27 mins ago
lthompsonlthompson
1169
$endgroup$
add a comment |
$begingroup$
Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.
elementary-set-theory
asked 27 mins ago
lthompsonlthompson
1169
$endgroup$
add a comment |
$begingroup$
Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.
elementary-set-theory
asked 27 mins ago
lthompsonlthompson
1169
$endgroup$
Is there any set whose every subset is equal to the set itself? It seems like this isn't possible, but maybe something similar is possible.
elementary-set-theory
elementary-set-theory
asked 27 mins ago
lthompsonlthompson
1169
asked 27 mins ago
lthompsonlthompson
1169
asked 27 mins ago
lthompsonlthompson
1169
asked 27 mins ago
lthompsonlthompson
1169
asked 27 mins ago
lthompsonlthompson
1169
1169
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
In standard foundations (by which I mean ZF, or ZFC) the empty set works:
If $Ssubset emptyset$, then $S = emptyset$.
If you wish to do so otherwise, you’d violate the Axiom of Extensionality.
answered 20 mins ago
user458276user458276
743212
$endgroup$
add a comment |
$begingroup$
The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
$endgroup$
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%2f3137096%2fevery-subset-equal-to-original-set%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In standard foundations (by which I mean ZF, or ZFC) the empty set works:
If $Ssubset emptyset$, then $S = emptyset$.
If you wish to do so otherwise, you’d violate the Axiom of Extensionality.
answered 20 mins ago
user458276user458276
743212
$endgroup$
add a comment |
$begingroup$
In standard foundations (by which I mean ZF, or ZFC) the empty set works:
If $Ssubset emptyset$, then $S = emptyset$.
If you wish to do so otherwise, you’d violate the Axiom of Extensionality.
answered 20 mins ago
user458276user458276
743212
$endgroup$
add a comment |
$begingroup$
In standard foundations (by which I mean ZF, or ZFC) the empty set works:
If $Ssubset emptyset$, then $S = emptyset$.
If you wish to do so otherwise, you’d violate the Axiom of Extensionality.
answered 20 mins ago
user458276user458276
743212
$endgroup$
In standard foundations (by which I mean ZF, or ZFC) the empty set works:
If $Ssubset emptyset$, then $S = emptyset$.
If you wish to do so otherwise, you’d violate the Axiom of Extensionality.
answered 20 mins ago
user458276user458276
743212
answered 20 mins ago
user458276user458276
743212
answered 20 mins ago
user458276user458276
743212
answered 20 mins ago
user458276user458276
743212
743212
add a comment |
add a comment |
$begingroup$
The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
$endgroup$
add a comment |
$begingroup$
The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
$endgroup$
add a comment |
$begingroup$
The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
$endgroup$
The empty set has only itself as a subset. This is the only example because every set has the empty set as a subset.
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 20 mins ago
Ross MillikanRoss Millikan
298k24200373
298k24200373
add a comment |
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%2f3137096%2fevery-subset-equal-to-original-set%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
