Every subset equal to original set?Is the void set (∅) a proper subset of every set?Set theory: difference...
Skis versus snow shoes - when to choose which for travelling the backcountry?
Are there any other Chaos-worshipping races?
VAT refund for a conference ticket in Sweden
Book about a time-travel war fought by computers
What happened to QGIS 2.x LTR?
Citing contemporaneous (interlaced?) preprints
Called into a meeting and told we are being made redundant (laid off) and "not to share outside". Can I tell my partner?
Wrap all numerics in JSON with quotes
How can I handle a player who pre-plans arguments about my rulings on RAW?
A bug in Excel? Conditional formatting for marking duplicates also highlights unique value
Reason why dimensional travelling would be restricted
Where is the fallacy here?
What are all the squawk codes?
What is better: yes / no radio, or simple checkbox?
Why can't we make a perpetual motion machine by using a magnet to pull up a piece of metal, then letting it fall back down?
Sometimes a banana is just a banana
Why do members of Congress in committee hearings ask witnesses the same question multiple times?
What could trigger powerful quakes on icy world?
Plagiarism of code by other PhD student
Every subset equal to original set?
Why do phishing e-mails use faked e-mail addresses instead of the real one?
Six real numbers so that product of any five is the sixth one
How to make a *empty* field behaves like a *null* field when it comes to standard values?
How to kill a localhost:8080
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 39 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 39 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 39 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 39 mins ago
lthompsonlthompson
1169
asked 39 mins ago
lthompsonlthompson
1169
asked 39 mins ago
lthompsonlthompson
1169
asked 39 mins ago
lthompsonlthompson
1169
asked 39 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 33 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 32 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 33 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 33 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 33 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 33 mins ago
user458276user458276
743212
answered 33 mins ago
user458276user458276
743212
answered 33 mins ago
user458276user458276
743212
answered 33 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 32 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 32 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 32 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 32 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 32 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 32 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 32 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