Do I write for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
0
$begingroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3365
$endgroup$
add a comment |
0
$begingroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3365
$endgroup$
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
add a comment |
0
0
0
1
$begingroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3365
$endgroup$
When I want to say that if $x$ is even, then $x = 2k$, am I supposed to say for SOME $k in Bbb Z$ or for ALL $k in Bbb Z$?
linear-algebra
linear-algebra
asked Dec 8 '18 at 0:56
mingming
3365
asked Dec 8 '18 at 0:56
mingming
3365
asked Dec 8 '18 at 0:56
mingming
3365
asked Dec 8 '18 at 0:56
mingming
3365
asked Dec 8 '18 at 0:56
mingming
3365
3365
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
add a comment |
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
3
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03
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%2f3030576%2fdo-i-write-for-some-k-in-bbb-z-or-for-all-k-in-bbb-z%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%2f3030576%2fdo-i-write-for-some-k-in-bbb-z-or-for-all-k-in-bbb-z%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
3
$begingroup$
Need to say "some" since can't say $x=2k$ for all $k$ [makes no sense]
$endgroup$
– coffeemath
Dec 8 '18 at 0:58
$begingroup$
I'd say "There exists $kinBbb Z$ such that $x=2k$"... Which is both precise and easy to write in first order logic.
$endgroup$
– Saucy O'Path
Dec 8 '18 at 1:34
$begingroup$
Ask yourself what would be true for x if the statement were true for two different integers.
$endgroup$
– Joel Pereira
Dec 8 '18 at 2:03