Can a uncountable union of finite sets be uncountable?Uncountable Sets that can not be expressed as a disjoint union of two Uncountable setsUnion of Uncountably Many Uncountable SetsThe set of all finite subsets and the set of all infinite subsets of a countably infinite setdo all uncountable sets have same cardinality as real numbers?First Uncountable Ordinal Cofinality: Needs AC?Is it consistent that every set is the countable union of sets with smaller cardinality, or is it just alephs?Uncountable dense sets of reals without the axiom of choiceWriting uncountable set as union of finite sets $I_j$ with $I_j subseteq I_j+1$
Other than good shoes and a stick, what are some ways to preserve your knees on long hikes?
Exam design: give maximum score per question or not?
Floating Point XOR
Output Distinct Factor Cuboids
Where did Otto von Bismarck say "lying awake all night, hating"?
What was the earliest microcomputer Logo language implementation?
How often is duct tape used during crewed space missions?
Plausibility and performance of a composite longbow
Why is the UK still pressing on with Brexit?
Which block header fields are miners able to change in an effort to avoid having to recalculate the Merkle Root?
Are all article combinations valid patterns for "the" ɴᴏᴜɴ of "the" ɴᴏᴜɴ?
How to generate short fixed length cryptographic hashes?
How to give my students a straightedge instead of a ruler
Why do things cool off?
What if I don't know whether my program will be linked to a GPL library or not?
Amortized Loans seem to benefit the bank more than the customer
Three knights searching for a princess in a castle
Paradox regarding phase transitions in relativistic systems
How can I add a link on the "Structure" admin page?
What does the "capacitor into resistance" symbol mean?
How to convey to the people around me that I want to disengage myself from constant giving?
What is the source of "You can achieve a lot with hate, but even more with love" (Shakespeare?)
Do encumbered characters suffer any penalties when exploring and/or traveling?
Is the name of an interval between two notes unique and absolute?
Can a uncountable union of finite sets be uncountable?
Uncountable Sets that can not be expressed as a disjoint union of two Uncountable setsUnion of Uncountably Many Uncountable SetsThe set of all finite subsets and the set of all infinite subsets of a countably infinite setdo all uncountable sets have same cardinality as real numbers?First Uncountable Ordinal Cofinality: Needs AC?Is it consistent that every set is the countable union of sets with smaller cardinality, or is it just alephs?Uncountable dense sets of reals without the axiom of choiceWriting uncountable set as union of finite sets $I_j$ with $I_j subseteq I_j+1$
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
A finite or countable union of finite sets is countable, then what about uncountable union of finite sets?
set-theory
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
$endgroup$
add a comment
|
$begingroup$
A finite or countable union of finite sets is countable, then what about uncountable union of finite sets?
set-theory
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
$endgroup$
9
$begingroup$
$mathbbR=bigcup_x in mathbbRx$.
$endgroup$
– Mindlack
8 hours ago
$begingroup$
Just for fun,): a countable union of countable sets is countable.
$endgroup$
– dmtri
8 hours ago
$begingroup$
The union of uncountable copies of the empty set is... the empty set.
$endgroup$
– Martín-Blas Pérez Pinilla
7 hours ago
$begingroup$
It can be empty, finite, countable or uncountable.
$endgroup$
– Eric Duminil
1 min ago
add a comment
|
$begingroup$
A finite or countable union of finite sets is countable, then what about uncountable union of finite sets?
set-theory
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
$endgroup$
A finite or countable union of finite sets is countable, then what about uncountable union of finite sets?
set-theory
set-theory
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
asked 8 hours ago
Cathy Cathy
3502 silver badges9 bronze badges
3502 silver badges9 bronze badges
9
$begingroup$
$mathbbR=bigcup_x in mathbbRx$.
$endgroup$
– Mindlack
8 hours ago
$begingroup$
Just for fun,): a countable union of countable sets is countable.
$endgroup$
– dmtri
8 hours ago
$begingroup$
The union of uncountable copies of the empty set is... the empty set.
$endgroup$
– Martín-Blas Pérez Pinilla
7 hours ago
$begingroup$
It can be empty, finite, countable or uncountable.
$endgroup$
– Eric Duminil
1 min ago
add a comment
|
9
$begingroup$
$mathbbR=bigcup_x in mathbbRx$.
$endgroup$
– Mindlack
8 hours ago
$begingroup$
Just for fun,): a countable union of countable sets is countable.
$endgroup$
– dmtri
8 hours ago
$begingroup$
The union of uncountable copies of the empty set is... the empty set.
$endgroup$
– Martín-Blas Pérez Pinilla
7 hours ago
$begingroup$
It can be empty, finite, countable or uncountable.
$endgroup$
– Eric Duminil
1 min ago
9
9
$begingroup$
$mathbbR=bigcup_x in mathbbRx$.
$endgroup$
– Mindlack
8 hours ago
$begingroup$
$mathbbR=bigcup_x in mathbbRx$.
$endgroup$
– Mindlack
8 hours ago
$begingroup$
Just for fun,): a countable union of countable sets is countable.
$endgroup$
– dmtri
8 hours ago
$begingroup$
Just for fun,): a countable union of countable sets is countable.
$endgroup$
– dmtri
8 hours ago
$begingroup$
The union of uncountable copies of the empty set is... the empty set.
$endgroup$
– Martín-Blas Pérez Pinilla
7 hours ago
$begingroup$
The union of uncountable copies of the empty set is... the empty set.
$endgroup$
– Martín-Blas Pérez Pinilla
7 hours ago
$begingroup$
It can be empty, finite, countable or uncountable.
$endgroup$
– Eric Duminil
1 min ago
$begingroup$
It can be empty, finite, countable or uncountable.
$endgroup$
– Eric Duminil
1 min ago
add a comment
|
1 Answer
1
active
oldest
votes
$begingroup$
$$mathbb R=bigcup_xinmathbb Rx .$$
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
$endgroup$
add a comment
|
Your Answer
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/4.0/"u003ecc by-sa 4.0 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%2f3358311%2fcan-a-uncountable-union-of-finite-sets-be-uncountable%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
$begingroup$
$$mathbb R=bigcup_xinmathbb Rx .$$
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
$endgroup$
add a comment
|
$begingroup$
$$mathbb R=bigcup_xinmathbb Rx .$$
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
$endgroup$
add a comment
|
$begingroup$
$$mathbb R=bigcup_xinmathbb Rx .$$
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
$endgroup$
$$mathbb R=bigcup_xinmathbb Rx .$$
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
answered 8 hours ago
Thomas ShelbyThomas Shelby
6,6763 gold badges10 silver badges32 bronze badges
6,6763 gold badges10 silver badges32 bronze badges
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%2f3358311%2fcan-a-uncountable-union-of-finite-sets-be-uncountable%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
9
$begingroup$
$mathbbR=bigcup_x in mathbbRx$.
$endgroup$
– Mindlack
8 hours ago
$begingroup$
Just for fun,): a countable union of countable sets is countable.
$endgroup$
– dmtri
8 hours ago
$begingroup$
The union of uncountable copies of the empty set is... the empty set.
$endgroup$
– Martín-Blas Pérez Pinilla
7 hours ago
$begingroup$
It can be empty, finite, countable or uncountable.
$endgroup$
– Eric Duminil
1 min ago