Relation of divisibility {0,1,…,20} - Hasse diagram
I am trying to draw a Hasse diagram of divisibility but AFAIK it's not correct.
I connected 4 with 8 , 12 and 20.
6 with 18 and 12,
5 with 15 and 10,
3 with 9, 6, 15
H
2 with 6, 4, 10 and 14.
1 with prime numbers
Is this correct? Thanks. The rest should correct.
relations
add a comment |
I am trying to draw a Hasse diagram of divisibility but AFAIK it's not correct.
I connected 4 with 8 , 12 and 20.
6 with 18 and 12,
5 with 15 and 10,
3 with 9, 6, 15
H
2 with 6, 4, 10 and 14.
1 with prime numbers
Is this correct? Thanks. The rest should correct.
relations
What is your diagram supposed to show? All the numbers you've listed does divide each other as described, but it's not all division relationships in that set, but "The rest should correct." could cover the missing divisors, meaning that what you've done is correct.
– Henrik
Nov 18 at 15:53
add a comment |
I am trying to draw a Hasse diagram of divisibility but AFAIK it's not correct.
I connected 4 with 8 , 12 and 20.
6 with 18 and 12,
5 with 15 and 10,
3 with 9, 6, 15
H
2 with 6, 4, 10 and 14.
1 with prime numbers
Is this correct? Thanks. The rest should correct.
relations
I am trying to draw a Hasse diagram of divisibility but AFAIK it's not correct.
I connected 4 with 8 , 12 and 20.
6 with 18 and 12,
5 with 15 and 10,
3 with 9, 6, 15
H
2 with 6, 4, 10 and 14.
1 with prime numbers
Is this correct? Thanks. The rest should correct.
relations
relations
edited Nov 18 at 15:43
Bernard
118k639112
118k639112
asked Nov 18 at 15:36
Shelley
92
92
What is your diagram supposed to show? All the numbers you've listed does divide each other as described, but it's not all division relationships in that set, but "The rest should correct." could cover the missing divisors, meaning that what you've done is correct.
– Henrik
Nov 18 at 15:53
add a comment |
What is your diagram supposed to show? All the numbers you've listed does divide each other as described, but it's not all division relationships in that set, but "The rest should correct." could cover the missing divisors, meaning that what you've done is correct.
– Henrik
Nov 18 at 15:53
What is your diagram supposed to show? All the numbers you've listed does divide each other as described, but it's not all division relationships in that set, but "The rest should correct." could cover the missing divisors, meaning that what you've done is correct.
– Henrik
Nov 18 at 15:53
What is your diagram supposed to show? All the numbers you've listed does divide each other as described, but it's not all division relationships in that set, but "The rest should correct." could cover the missing divisors, meaning that what you've done is correct.
– Henrik
Nov 18 at 15:53
add a comment |
1 Answer
1
active
oldest
votes
You're missing many connections (each element should be connected to one that's greater and minimal among the greater elements). You're also forgetting about $0$.
At the lowest level you have to place the minimum, that is, $1$.
At the next level, the primes: $2$, $3$, $5$, $7$, $11$, $13$, $17$ and $19$.
Next level, the products of two (not necessarily distinct) primes, that is, $4$, $6$, $9$, $10$, $14$, $15$.
Next level, the products of three primes: $8$, $12$, $18$, $20$.
Last level, the maximum, that is, $0$.
Connections:
$1$ is connected to every term at the next level (the primes);
$2$ is connected to $4$, $6$, $10$;
$3$ is connected to $6$, $9$, $15$;
$5$ is connected to $10$, $15$, $20$;
$7$ is connected to $14$;
$11$, $13$, $17$, $19$ are connected to $0$;
$4$ is connected to $8$, $12$, $20$;
$6$ is connected to $12$, $18$;
$10$ is connected to $20$;
$8$, $12$, $18$, $20$ are connected to $0$.
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%2f3003686%2frelation-of-divisibility-0-1-20-hasse-diagram%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
You're missing many connections (each element should be connected to one that's greater and minimal among the greater elements). You're also forgetting about $0$.
At the lowest level you have to place the minimum, that is, $1$.
At the next level, the primes: $2$, $3$, $5$, $7$, $11$, $13$, $17$ and $19$.
Next level, the products of two (not necessarily distinct) primes, that is, $4$, $6$, $9$, $10$, $14$, $15$.
Next level, the products of three primes: $8$, $12$, $18$, $20$.
Last level, the maximum, that is, $0$.
Connections:
$1$ is connected to every term at the next level (the primes);
$2$ is connected to $4$, $6$, $10$;
$3$ is connected to $6$, $9$, $15$;
$5$ is connected to $10$, $15$, $20$;
$7$ is connected to $14$;
$11$, $13$, $17$, $19$ are connected to $0$;
$4$ is connected to $8$, $12$, $20$;
$6$ is connected to $12$, $18$;
$10$ is connected to $20$;
$8$, $12$, $18$, $20$ are connected to $0$.
add a comment |
You're missing many connections (each element should be connected to one that's greater and minimal among the greater elements). You're also forgetting about $0$.
At the lowest level you have to place the minimum, that is, $1$.
At the next level, the primes: $2$, $3$, $5$, $7$, $11$, $13$, $17$ and $19$.
Next level, the products of two (not necessarily distinct) primes, that is, $4$, $6$, $9$, $10$, $14$, $15$.
Next level, the products of three primes: $8$, $12$, $18$, $20$.
Last level, the maximum, that is, $0$.
Connections:
$1$ is connected to every term at the next level (the primes);
$2$ is connected to $4$, $6$, $10$;
$3$ is connected to $6$, $9$, $15$;
$5$ is connected to $10$, $15$, $20$;
$7$ is connected to $14$;
$11$, $13$, $17$, $19$ are connected to $0$;
$4$ is connected to $8$, $12$, $20$;
$6$ is connected to $12$, $18$;
$10$ is connected to $20$;
$8$, $12$, $18$, $20$ are connected to $0$.
add a comment |
You're missing many connections (each element should be connected to one that's greater and minimal among the greater elements). You're also forgetting about $0$.
At the lowest level you have to place the minimum, that is, $1$.
At the next level, the primes: $2$, $3$, $5$, $7$, $11$, $13$, $17$ and $19$.
Next level, the products of two (not necessarily distinct) primes, that is, $4$, $6$, $9$, $10$, $14$, $15$.
Next level, the products of three primes: $8$, $12$, $18$, $20$.
Last level, the maximum, that is, $0$.
Connections:
$1$ is connected to every term at the next level (the primes);
$2$ is connected to $4$, $6$, $10$;
$3$ is connected to $6$, $9$, $15$;
$5$ is connected to $10$, $15$, $20$;
$7$ is connected to $14$;
$11$, $13$, $17$, $19$ are connected to $0$;
$4$ is connected to $8$, $12$, $20$;
$6$ is connected to $12$, $18$;
$10$ is connected to $20$;
$8$, $12$, $18$, $20$ are connected to $0$.
You're missing many connections (each element should be connected to one that's greater and minimal among the greater elements). You're also forgetting about $0$.
At the lowest level you have to place the minimum, that is, $1$.
At the next level, the primes: $2$, $3$, $5$, $7$, $11$, $13$, $17$ and $19$.
Next level, the products of two (not necessarily distinct) primes, that is, $4$, $6$, $9$, $10$, $14$, $15$.
Next level, the products of three primes: $8$, $12$, $18$, $20$.
Last level, the maximum, that is, $0$.
Connections:
$1$ is connected to every term at the next level (the primes);
$2$ is connected to $4$, $6$, $10$;
$3$ is connected to $6$, $9$, $15$;
$5$ is connected to $10$, $15$, $20$;
$7$ is connected to $14$;
$11$, $13$, $17$, $19$ are connected to $0$;
$4$ is connected to $8$, $12$, $20$;
$6$ is connected to $12$, $18$;
$10$ is connected to $20$;
$8$, $12$, $18$, $20$ are connected to $0$.
answered Nov 18 at 17:44
egreg
178k1484201
178k1484201
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.
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%2f3003686%2frelation-of-divisibility-0-1-20-hasse-diagram%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
What is your diagram supposed to show? All the numbers you've listed does divide each other as described, but it's not all division relationships in that set, but "The rest should correct." could cover the missing divisors, meaning that what you've done is correct.
– Henrik
Nov 18 at 15:53