find a map which satisfies the following
hey I have to find a map, which works like this: map $f$ must map $$0 to (0,0), 1 to (0,1),2 to (0,2), 3 to (1,0), 4 to (1,1), 5 to (1,2), 6 to (2,0), 7to(2,1)$$ and finally $ 8to (2,2)$.
I was thinking something like $f(i) to (i mod 3, i+1mod 3)$ would work, but there are some exceptions... does anyone have any idea?
functions modular-arithmetic
asked Dec 3 '18 at 9:33
mandella
717521
add a comment |
hey I have to find a map, which works like this: map $f$ must map $$0 to (0,0), 1 to (0,1),2 to (0,2), 3 to (1,0), 4 to (1,1), 5 to (1,2), 6 to (2,0), 7to(2,1)$$ and finally $ 8to (2,2)$.
I was thinking something like $f(i) to (i mod 3, i+1mod 3)$ would work, but there are some exceptions... does anyone have any idea?
functions modular-arithmetic
asked Dec 3 '18 at 9:33
mandella
717521
add a comment |
hey I have to find a map, which works like this: map $f$ must map $$0 to (0,0), 1 to (0,1),2 to (0,2), 3 to (1,0), 4 to (1,1), 5 to (1,2), 6 to (2,0), 7to(2,1)$$ and finally $ 8to (2,2)$.
I was thinking something like $f(i) to (i mod 3, i+1mod 3)$ would work, but there are some exceptions... does anyone have any idea?
functions modular-arithmetic
asked Dec 3 '18 at 9:33
mandella
717521
hey I have to find a map, which works like this: map $f$ must map $$0 to (0,0), 1 to (0,1),2 to (0,2), 3 to (1,0), 4 to (1,1), 5 to (1,2), 6 to (2,0), 7to(2,1)$$ and finally $ 8to (2,2)$.
I was thinking something like $f(i) to (i mod 3, i+1mod 3)$ would work, but there are some exceptions... does anyone have any idea?
functions modular-arithmetic
functions modular-arithmetic
asked Dec 3 '18 at 9:33
mandella
717521
asked Dec 3 '18 at 9:33
mandella
717521
asked Dec 3 '18 at 9:33
mandella
717521
asked Dec 3 '18 at 9:33
mandella
717521
asked Dec 3 '18 at 9:33
mandella
717521
717521
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
If by finding a "map", you mean finding a rule of correspondence, then here is one answer:
$f:{0,1,...,8}rightarrowmathbb N: f(i)=(lfloor i/3 rfloor, i mod 3)$
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
1
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
1
perfect, thank you
– mandella
Dec 3 '18 at 9:52
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%2f3023834%2ffind-a-map-which-satisfies-the-following%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
If by finding a "map", you mean finding a rule of correspondence, then here is one answer:
$f:{0,1,...,8}rightarrowmathbb N: f(i)=(lfloor i/3 rfloor, i mod 3)$
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
1
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
1
perfect, thank you
– mandella
Dec 3 '18 at 9:52
add a comment |
If by finding a "map", you mean finding a rule of correspondence, then here is one answer:
$f:{0,1,...,8}rightarrowmathbb N: f(i)=(lfloor i/3 rfloor, i mod 3)$
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
1
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
1
perfect, thank you
– mandella
Dec 3 '18 at 9:52
add a comment |
If by finding a "map", you mean finding a rule of correspondence, then here is one answer:
$f:{0,1,...,8}rightarrowmathbb N: f(i)=(lfloor i/3 rfloor, i mod 3)$
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
If by finding a "map", you mean finding a rule of correspondence, then here is one answer:
$f:{0,1,...,8}rightarrowmathbb N: f(i)=(lfloor i/3 rfloor, i mod 3)$
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
edited Dec 3 '18 at 9:51
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
answered Dec 3 '18 at 9:47
Shubham Johri
4,264717
4,264717
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
1
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
1
perfect, thank you
– mandella
Dec 3 '18 at 9:52
add a comment |
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
1
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
1
perfect, thank you
– mandella
Dec 3 '18 at 9:52
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
That is what I meant, but $f(5) = (1,5)$ does not satisfy my condition.
– mandella
Dec 3 '18 at 9:48
1
1
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
Sorry, that was a typo.
– Shubham Johri
Dec 3 '18 at 9:51
1
1
perfect, thank you
– mandella
Dec 3 '18 at 9:52
perfect, thank you
– mandella
Dec 3 '18 at 9:52
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3023834%2ffind-a-map-which-satisfies-the-following%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
