Function notation when $f^n=g^n$ at some $n$?
$begingroup$
What is the proper terminology / symbol to use for a function that reaches some point/value or a variable? Not necessarily converge to it, but passes it somehow?
Example
For $xinmathbb{N}$. Set initially $x_0=2$.
Iterating the function $f(x) = 2x$ will at some point reach the value $64$ for example: ${4,8,16,32,underline{64},128,256,..}$. For this case, $f(x)$ passes $x_0^6$ ? (i.e. $x_0$ raised to $6$).
Or do you say, for some $n$ the function $f^n(x)$ will reach or pass the value $64$ or $x_0^6$?
If we use two functions, is it possible to say the function $f^n$ passes through function $g^n$ at some $n$? or $f^n = g^n$ at some $n$ ?
functions notation terminology
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
$endgroup$
add a comment |
$begingroup$
What is the proper terminology / symbol to use for a function that reaches some point/value or a variable? Not necessarily converge to it, but passes it somehow?
Example
For $xinmathbb{N}$. Set initially $x_0=2$.
Iterating the function $f(x) = 2x$ will at some point reach the value $64$ for example: ${4,8,16,32,underline{64},128,256,..}$. For this case, $f(x)$ passes $x_0^6$ ? (i.e. $x_0$ raised to $6$).
Or do you say, for some $n$ the function $f^n(x)$ will reach or pass the value $64$ or $x_0^6$?
If we use two functions, is it possible to say the function $f^n$ passes through function $g^n$ at some $n$? or $f^n = g^n$ at some $n$ ?
functions notation terminology
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
$endgroup$
add a comment |
$begingroup$
What is the proper terminology / symbol to use for a function that reaches some point/value or a variable? Not necessarily converge to it, but passes it somehow?
Example
For $xinmathbb{N}$. Set initially $x_0=2$.
Iterating the function $f(x) = 2x$ will at some point reach the value $64$ for example: ${4,8,16,32,underline{64},128,256,..}$. For this case, $f(x)$ passes $x_0^6$ ? (i.e. $x_0$ raised to $6$).
Or do you say, for some $n$ the function $f^n(x)$ will reach or pass the value $64$ or $x_0^6$?
If we use two functions, is it possible to say the function $f^n$ passes through function $g^n$ at some $n$? or $f^n = g^n$ at some $n$ ?
functions notation terminology
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
$endgroup$
What is the proper terminology / symbol to use for a function that reaches some point/value or a variable? Not necessarily converge to it, but passes it somehow?
Example
For $xinmathbb{N}$. Set initially $x_0=2$.
Iterating the function $f(x) = 2x$ will at some point reach the value $64$ for example: ${4,8,16,32,underline{64},128,256,..}$. For this case, $f(x)$ passes $x_0^6$ ? (i.e. $x_0$ raised to $6$).
Or do you say, for some $n$ the function $f^n(x)$ will reach or pass the value $64$ or $x_0^6$?
If we use two functions, is it possible to say the function $f^n$ passes through function $g^n$ at some $n$? or $f^n = g^n$ at some $n$ ?
functions notation terminology
functions notation terminology
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
asked Dec 14 '18 at 16:13
Natural Number GuyNatural Number Guy
500518
500518
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
To answer the question in the body, we say that "$64$ is in the orbit of $2$ under $f$".
More generally, if $f^n(x_0)=y$, then say that "$y$ is in the orbit of $x_0$ under $f$".
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
$endgroup$
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%2f3039556%2ffunction-notation-when-fn-gn-at-some-n%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
$begingroup$
To answer the question in the body, we say that "$64$ is in the orbit of $2$ under $f$".
More generally, if $f^n(x_0)=y$, then say that "$y$ is in the orbit of $x_0$ under $f$".
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
$endgroup$
add a comment |
$begingroup$
To answer the question in the body, we say that "$64$ is in the orbit of $2$ under $f$".
More generally, if $f^n(x_0)=y$, then say that "$y$ is in the orbit of $x_0$ under $f$".
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
$endgroup$
add a comment |
$begingroup$
To answer the question in the body, we say that "$64$ is in the orbit of $2$ under $f$".
More generally, if $f^n(x_0)=y$, then say that "$y$ is in the orbit of $x_0$ under $f$".
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
$endgroup$
To answer the question in the body, we say that "$64$ is in the orbit of $2$ under $f$".
More generally, if $f^n(x_0)=y$, then say that "$y$ is in the orbit of $x_0$ under $f$".
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
answered Dec 14 '18 at 16:44
lhflhf
166k10171396
166k10171396
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%2f3039556%2ffunction-notation-when-fn-gn-at-some-n%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
