Every subset equal to original set?Is the void set (∅) a proper subset of every set?Set theory: difference...
When was drinking water recognized as crucial in marathon running?
Sometimes a banana is just a banana
Should we avoid writing fiction about historical events without extensive research?
How can I create a Table like this in Latex?
Pure Functions: Does "No Side Effects" Imply "Always Same Output, Given Same Input"?
What could trigger powerful quakes on icy world?
Citing contemporaneous (interlaced?) preprints
Are paired adjectives bad style?
At what level can a party fight a mimic?
Non-Italian European mafias in USA?
If nine coins are tossed, what is the probability that the number of heads is even?
Reason why dimensional travelling would be restricted
Is there a frame of reference in which I was born before I was conceived?
Every subset equal to original set?
I can't die. Who am I?
In Adventurer's League, is it possible to keep the Ring of Winter if you manage to acquire it in the Tomb of Annihilation adventure?
Do higher etale homotopy groups of spectrum of a field always vanish?
Starting index at zero
What does @RC mean in SSDT SQL Server Unit Testing?
How do you say "powers of ten"?
Is there a full canon version of Tyrion's jackass/honeycomb joke?
If a set is open, does that imply that it has no boundary points?
Why do phishing e-mails use faked e-mail addresses instead of the real one?
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?
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 31 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 31 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 31 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 31 mins ago
lthompsonlthompson
1169
asked 31 mins ago
lthompsonlthompson
1169
asked 31 mins ago
lthompsonlthompson
1169
asked 31 mins ago
lthompsonlthompson
1169
asked 31 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 25 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 24 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 25 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 25 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 25 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 25 mins ago
user458276user458276
743212
answered 25 mins ago
user458276user458276
743212
answered 25 mins ago
user458276user458276
743212
answered 25 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 24 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 24 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 24 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 24 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 24 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 24 mins ago
Ross MillikanRoss Millikan
298k24200373
answered 24 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
