number of words in language $L subset Sigma$
$begingroup$
I had my lecture today about decidable languages and as I am reviewing the material I have from the university, I got quite confused about the following definition:
$emptyset$ doesn't contain any words and is called the empty set. $Sigma^*$ contains all possible languages from $Sigma$, and $Sigma$ contains all words of length 1.
Does this mean if I define a Language $L subset Sigma$, $L$ is the set of all Languages of length 1?
Specifically, if $Sigma={0,1}$, then the length $L$ is 2?
formal-languages regular-language regular-expressions
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
$endgroup$
add a comment |
$begingroup$
I had my lecture today about decidable languages and as I am reviewing the material I have from the university, I got quite confused about the following definition:
$emptyset$ doesn't contain any words and is called the empty set. $Sigma^*$ contains all possible languages from $Sigma$, and $Sigma$ contains all words of length 1.
Does this mean if I define a Language $L subset Sigma$, $L$ is the set of all Languages of length 1?
Specifically, if $Sigma={0,1}$, then the length $L$ is 2?
formal-languages regular-language regular-expressions
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
$endgroup$
2
$begingroup$
$Sigma$ means the two words $0,1$, $Sigma^2$ means the four words $00,01,10,11$, etc. $Sigma^* = Sigma cup Sigma^2 cup Sigma^3 cup...$.
$endgroup$
– copper.hat
Jan 8 at 18:27
$begingroup$
It is not clear what you mean by the length of a language. Also, if $L in Sigma$ then either $L=0$ or $L=1$. Perhaps you mean $L subset Sigma$?
$endgroup$
– copper.hat
Jan 8 at 18:29
$begingroup$
@copper.hat yes I meant $subset$, edited the question. Thank you for your first comment, this clears the issue :)
$endgroup$
– Courtney Mill
Jan 8 at 18:34
add a comment |
$begingroup$
I had my lecture today about decidable languages and as I am reviewing the material I have from the university, I got quite confused about the following definition:
$emptyset$ doesn't contain any words and is called the empty set. $Sigma^*$ contains all possible languages from $Sigma$, and $Sigma$ contains all words of length 1.
Does this mean if I define a Language $L subset Sigma$, $L$ is the set of all Languages of length 1?
Specifically, if $Sigma={0,1}$, then the length $L$ is 2?
formal-languages regular-language regular-expressions
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
$endgroup$
I had my lecture today about decidable languages and as I am reviewing the material I have from the university, I got quite confused about the following definition:
$emptyset$ doesn't contain any words and is called the empty set. $Sigma^*$ contains all possible languages from $Sigma$, and $Sigma$ contains all words of length 1.
Does this mean if I define a Language $L subset Sigma$, $L$ is the set of all Languages of length 1?
Specifically, if $Sigma={0,1}$, then the length $L$ is 2?
formal-languages regular-language regular-expressions
formal-languages regular-language regular-expressions
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
edited Jan 8 at 18:33
Courtney Mill
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
asked Jan 8 at 18:15
Courtney MillCourtney Mill
527
527
2
$begingroup$
$Sigma$ means the two words $0,1$, $Sigma^2$ means the four words $00,01,10,11$, etc. $Sigma^* = Sigma cup Sigma^2 cup Sigma^3 cup...$.
$endgroup$
– copper.hat
Jan 8 at 18:27
$begingroup$
It is not clear what you mean by the length of a language. Also, if $L in Sigma$ then either $L=0$ or $L=1$. Perhaps you mean $L subset Sigma$?
$endgroup$
– copper.hat
Jan 8 at 18:29
$begingroup$
@copper.hat yes I meant $subset$, edited the question. Thank you for your first comment, this clears the issue :)
$endgroup$
– Courtney Mill
Jan 8 at 18:34
add a comment |
2
$begingroup$
$Sigma$ means the two words $0,1$, $Sigma^2$ means the four words $00,01,10,11$, etc. $Sigma^* = Sigma cup Sigma^2 cup Sigma^3 cup...$.
$endgroup$
– copper.hat
Jan 8 at 18:27
$begingroup$
It is not clear what you mean by the length of a language. Also, if $L in Sigma$ then either $L=0$ or $L=1$. Perhaps you mean $L subset Sigma$?
$endgroup$
– copper.hat
Jan 8 at 18:29
$begingroup$
@copper.hat yes I meant $subset$, edited the question. Thank you for your first comment, this clears the issue :)
$endgroup$
– Courtney Mill
Jan 8 at 18:34
2
2
$begingroup$
$Sigma$ means the two words $0,1$, $Sigma^2$ means the four words $00,01,10,11$, etc. $Sigma^* = Sigma cup Sigma^2 cup Sigma^3 cup...$.
$endgroup$
– copper.hat
Jan 8 at 18:27
$begingroup$
$Sigma$ means the two words $0,1$, $Sigma^2$ means the four words $00,01,10,11$, etc. $Sigma^* = Sigma cup Sigma^2 cup Sigma^3 cup...$.
$endgroup$
– copper.hat
Jan 8 at 18:27
$begingroup$
It is not clear what you mean by the length of a language. Also, if $L in Sigma$ then either $L=0$ or $L=1$. Perhaps you mean $L subset Sigma$?
$endgroup$
– copper.hat
Jan 8 at 18:29
$begingroup$
It is not clear what you mean by the length of a language. Also, if $L in Sigma$ then either $L=0$ or $L=1$. Perhaps you mean $L subset Sigma$?
$endgroup$
– copper.hat
Jan 8 at 18:29
$begingroup$
@copper.hat yes I meant $subset$, edited the question. Thank you for your first comment, this clears the issue :)
$endgroup$
– Courtney Mill
Jan 8 at 18:34
$begingroup$
@copper.hat yes I meant $subset$, edited the question. Thank you for your first comment, this clears the issue :)
$endgroup$
– Courtney Mill
Jan 8 at 18:34
add a comment |
0
active
oldest
votes
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/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%2f3066532%2fnumber-of-words-in-language-l-subset-sigma%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3066532%2fnumber-of-words-in-language-l-subset-sigma%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
2
$begingroup$
$Sigma$ means the two words $0,1$, $Sigma^2$ means the four words $00,01,10,11$, etc. $Sigma^* = Sigma cup Sigma^2 cup Sigma^3 cup...$.
$endgroup$
– copper.hat
Jan 8 at 18:27
$begingroup$
It is not clear what you mean by the length of a language. Also, if $L in Sigma$ then either $L=0$ or $L=1$. Perhaps you mean $L subset Sigma$?
$endgroup$
– copper.hat
Jan 8 at 18:29
$begingroup$
@copper.hat yes I meant $subset$, edited the question. Thank you for your first comment, this clears the issue :)
$endgroup$
– Courtney Mill
Jan 8 at 18:34