Mixing
Ordered Sequence to Set Definition
$begingroup$
From Why ordered sequences can be reduced to sets?
$$ (x,y):={{x},{x,y}}$$
What's the more general equation to convert ordered sequences to sets?
What about $(x, y, z, ...)$?
sequences-and-series elementary-set-theory
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
$endgroup$
add a comment |
$begingroup$
From Why ordered sequences can be reduced to sets?
$$ (x,y):={{x},{x,y}}$$
What's the more general equation to convert ordered sequences to sets?
What about $(x, y, z, ...)$?
sequences-and-series elementary-set-theory
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
$endgroup$
add a comment |
$begingroup$
From Why ordered sequences can be reduced to sets?
$$ (x,y):={{x},{x,y}}$$
What's the more general equation to convert ordered sequences to sets?
What about $(x, y, z, ...)$?
sequences-and-series elementary-set-theory
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
$endgroup$
From Why ordered sequences can be reduced to sets?
$$ (x,y):={{x},{x,y}}$$
What's the more general equation to convert ordered sequences to sets?
What about $(x, y, z, ...)$?
sequences-and-series elementary-set-theory
sequences-and-series elementary-set-theory
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
edited Jan 10 at 5:06
Andrés E. Caicedo
65.3k8158247
65.3k8158247
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
asked Jan 9 at 23:24
A_for_ AbacusA_for_ Abacus
955925
955925
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Two options: either define $(x_1,x_2,ldots,x_n)$ inductively as $(x_1,(x_2,ldots,x_n))$, or define it as ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n}}$, and define $(x_1,x_2,x_3,ldots)$, therefore, to be ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n},ldots}$.
answered Jan 9 at 23:27
user3482749user3482749
4,256919
$endgroup$
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
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%2f3068062%2fordered-sequence-to-set-definition%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
$begingroup$
Two options: either define $(x_1,x_2,ldots,x_n)$ inductively as $(x_1,(x_2,ldots,x_n))$, or define it as ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n}}$, and define $(x_1,x_2,x_3,ldots)$, therefore, to be ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n},ldots}$.
answered Jan 9 at 23:27
user3482749user3482749
4,256919
$endgroup$
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
add a comment |
$begingroup$
Two options: either define $(x_1,x_2,ldots,x_n)$ inductively as $(x_1,(x_2,ldots,x_n))$, or define it as ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n}}$, and define $(x_1,x_2,x_3,ldots)$, therefore, to be ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n},ldots}$.
answered Jan 9 at 23:27
user3482749user3482749
4,256919
$endgroup$
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
add a comment |
$begingroup$
Two options: either define $(x_1,x_2,ldots,x_n)$ inductively as $(x_1,(x_2,ldots,x_n))$, or define it as ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n}}$, and define $(x_1,x_2,x_3,ldots)$, therefore, to be ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n},ldots}$.
answered Jan 9 at 23:27
user3482749user3482749
4,256919
$endgroup$
Two options: either define $(x_1,x_2,ldots,x_n)$ inductively as $(x_1,(x_2,ldots,x_n))$, or define it as ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n}}$, and define $(x_1,x_2,x_3,ldots)$, therefore, to be ${{x_1},{x_1,x_2},ldots,{x_1,ldots,x_n},ldots}$.
answered Jan 9 at 23:27
user3482749user3482749
4,256919
answered Jan 9 at 23:27
user3482749user3482749
4,256919
answered Jan 9 at 23:27
user3482749user3482749
4,256919
answered Jan 9 at 23:27
user3482749user3482749
4,256919
4,256919
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
add a comment |
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
$begingroup$
ah, makes much more sense when I see the big picture.
$endgroup$
– A_for_ Abacus
Jan 9 at 23:36
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%2f3068062%2fordered-sequence-to-set-definition%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
