Let $S$ be a subset of positive integers. Show that no such set $S$ exist.
0
Let $S$ be a subset of positive integers, such that for any positive integer $n$, there exist a unique pair of integer of $a, b$ in $S$ such that $a+2b=n$. Show that no such set $S$ exist. (Hint: Show that it has no minimal element)
combinatorics
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
add a comment |
0
Let $S$ be a subset of positive integers, such that for any positive integer $n$, there exist a unique pair of integer of $a, b$ in $S$ such that $a+2b=n$. Show that no such set $S$ exist. (Hint: Show that it has no minimal element)
combinatorics
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
2
Welcome to MSE! This seems to be a homework question; you'll find that "do my homework" questions are generally not well-received here. Please edit the question to include your progress. This will show other users that you have actually attempted the problem and put some effort into it, as well as allow them to help you based on where you are stuck.
– platty
Dec 1 '18 at 6:49
5
Are you sure that you have the problem correct? Taking $n = 1$ should show that this immediately fails.
– platty
Dec 1 '18 at 6:50
add a comment |
0
0
0
Let $S$ be a subset of positive integers, such that for any positive integer $n$, there exist a unique pair of integer of $a, b$ in $S$ such that $a+2b=n$. Show that no such set $S$ exist. (Hint: Show that it has no minimal element)
combinatorics
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
Let $S$ be a subset of positive integers, such that for any positive integer $n$, there exist a unique pair of integer of $a, b$ in $S$ such that $a+2b=n$. Show that no such set $S$ exist. (Hint: Show that it has no minimal element)
combinatorics
combinatorics
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
asked Dec 1 '18 at 6:47
tedzzztedzzz
1
1
2
Welcome to MSE! This seems to be a homework question; you'll find that "do my homework" questions are generally not well-received here. Please edit the question to include your progress. This will show other users that you have actually attempted the problem and put some effort into it, as well as allow them to help you based on where you are stuck.
– platty
Dec 1 '18 at 6:49
5
Are you sure that you have the problem correct? Taking $n = 1$ should show that this immediately fails.
– platty
Dec 1 '18 at 6:50
add a comment |
2
Welcome to MSE! This seems to be a homework question; you'll find that "do my homework" questions are generally not well-received here. Please edit the question to include your progress. This will show other users that you have actually attempted the problem and put some effort into it, as well as allow them to help you based on where you are stuck.
– platty
Dec 1 '18 at 6:49
5
Are you sure that you have the problem correct? Taking $n = 1$ should show that this immediately fails.
– platty
Dec 1 '18 at 6:50
2
2
Welcome to MSE! This seems to be a homework question; you'll find that "do my homework" questions are generally not well-received here. Please edit the question to include your progress. This will show other users that you have actually attempted the problem and put some effort into it, as well as allow them to help you based on where you are stuck.
– platty
Dec 1 '18 at 6:49
Welcome to MSE! This seems to be a homework question; you'll find that "do my homework" questions are generally not well-received here. Please edit the question to include your progress. This will show other users that you have actually attempted the problem and put some effort into it, as well as allow them to help you based on where you are stuck.
– platty
Dec 1 '18 at 6:49
5
5
Are you sure that you have the problem correct? Taking $n = 1$ should show that this immediately fails.
– platty
Dec 1 '18 at 6:50
Are you sure that you have the problem correct? Taking $n = 1$ should show that this immediately fails.
– platty
Dec 1 '18 at 6:50
add a comment |
0
active
oldest
votes
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
});
}
});
draft saved
draft discarded
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%2f3021072%2flet-s-be-a-subset-of-positive-integers-show-that-no-such-set-s-exist%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
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3021072%2flet-s-be-a-subset-of-positive-integers-show-that-no-such-set-s-exist%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
Welcome to MSE! This seems to be a homework question; you'll find that "do my homework" questions are generally not well-received here. Please edit the question to include your progress. This will show other users that you have actually attempted the problem and put some effort into it, as well as allow them to help you based on where you are stuck.
– platty
Dec 1 '18 at 6:49
5
Are you sure that you have the problem correct? Taking $n = 1$ should show that this immediately fails.
– platty
Dec 1 '18 at 6:50