Decomposing $f + g > t$ The 2019 Stack Overflow Developer Survey Results Are In Unicorn Meta Zoo #1: Why another podcast? Announcing the arrival of Valued Associate #679: Cesar ManaraMinimal dense subset of $mathbbQ cap [0,1]$A classic example in measure theory, hold the measure theoryStep-by-step help using the distributive law in set theoryProving set function is measureCheck the identity $Acap (B - C)=(Acap B) - (Acap C)$Classification of an open set in realSuppose $A^text' $ is the set of limit point of $A$. Prove $A^text' $ is closed set.Show finite unions of rectangles form an algebraSymmetric difference as a equivalent relation-equivalence classesReformulation of intersection of two unions
Mortgage adviser recommends a longer term than necessary combined with overpayments
Button changing its text & action. Good or terrible?
Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?
Is there a way to generate uniformly distributed points on a sphere from a fixed amount of random real numbers per point?
How to determine omitted units in a publication
For what reasons would an animal species NOT cross a *horizontal* land bridge?
Do working physicists consider Newtonian mechanics to be "falsified"?
Presidential Pardon
Simulating Exploding Dice
How did the crowd guess the pentatonic scale in Bobby McFerrin's presentation?
What does "spokes" mean in this context?
Student Loan from years ago pops up and is taking my salary
Can a flute soloist sit?
Is this wall load bearing? Blueprints and photos attached
Why doesn't shell automatically fix "useless use of cat"?
What force causes entropy to increase?
My body leaves; my core can stay
Why did Peik Lin say, "I'm not an animal"?
What can I do if neighbor is blocking my solar panels intentionally?
How to support a colleague who finds meetings extremely tiring?
"is" operation returns false even though two objects have same id
One-dimensional Japanese puzzle
How many cones with angle theta can I pack into the unit sphere?
How to make Illustrator type tool selection automatically adapt with text length
Decomposing $f + g > t$
The 2019 Stack Overflow Developer Survey Results Are In
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraMinimal dense subset of $mathbbQ cap [0,1]$A classic example in measure theory, hold the measure theoryStep-by-step help using the distributive law in set theoryProving set function is measureCheck the identity $Acap (B - C)=(Acap B) - (Acap C)$Classification of an open set in realSuppose $A^text' $ is the set of limit point of $A$. Prove $A^text' $ is closed set.Show finite unions of rectangles form an algebraSymmetric difference as a equivalent relation-equivalence classesReformulation of intersection of two unions
$begingroup$
For this purpose of this question, define
$$
leftf > tright = left f(x) > tright
$$
I was told that
$$
leftf + g > t right = cup_r in mathbbQ leftf > r right cap leftg > t - r right
$$
I want to prove it, but I got stuck. The following equation seems to be a nice starting point, but I cannot prove it either.
$$
leftf + g > t right = cup_r in mathbbR leftf > r right cap leftg > t - r right
$$
Any hint?
real-analysis general-topology elementary-set-theory
asked Apr 8 at 6:34
nalzoknalzok
291217
$endgroup$
add a comment |
$begingroup$
For this purpose of this question, define
$$
leftf > tright = left f(x) > tright
$$
I was told that
$$
leftf + g > t right = cup_r in mathbbQ leftf > r right cap leftg > t - r right
$$
I want to prove it, but I got stuck. The following equation seems to be a nice starting point, but I cannot prove it either.
$$
leftf + g > t right = cup_r in mathbbR leftf > r right cap leftg > t - r right
$$
Any hint?
real-analysis general-topology elementary-set-theory
asked Apr 8 at 6:34
nalzoknalzok
291217
$endgroup$
add a comment |
$begingroup$
For this purpose of this question, define
$$
leftf > tright = left f(x) > tright
$$
I was told that
$$
leftf + g > t right = cup_r in mathbbQ leftf > r right cap leftg > t - r right
$$
I want to prove it, but I got stuck. The following equation seems to be a nice starting point, but I cannot prove it either.
$$
leftf + g > t right = cup_r in mathbbR leftf > r right cap leftg > t - r right
$$
Any hint?
real-analysis general-topology elementary-set-theory
asked Apr 8 at 6:34
nalzoknalzok
291217
$endgroup$
For this purpose of this question, define
$$
leftf > tright = left f(x) > tright
$$
I was told that
$$
leftf + g > t right = cup_r in mathbbQ leftf > r right cap leftg > t - r right
$$
I want to prove it, but I got stuck. The following equation seems to be a nice starting point, but I cannot prove it either.
$$
leftf + g > t right = cup_r in mathbbR leftf > r right cap leftg > t - r right
$$
Any hint?
real-analysis general-topology elementary-set-theory
real-analysis general-topology elementary-set-theory
asked Apr 8 at 6:34
nalzoknalzok
291217
asked Apr 8 at 6:34
nalzoknalzok
291217
asked Apr 8 at 6:34
nalzoknalzok
291217
asked Apr 8 at 6:34
nalzoknalzok
291217
asked Apr 8 at 6:34
nalzoknalzok
291217
291217
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Write $f(x)+g(x) >t$ as $f(x) >t-g(x)$. Since there is a rational number between any two real numbers we can find $r in mathbb Q$ such that $f(x) >r >t-g(x)$. Can you finish the proof now?
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
$endgroup$
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
add a comment |
Your Answer
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%2f3179254%2fdecomposing-f-g-t%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
$begingroup$
Write $f(x)+g(x) >t$ as $f(x) >t-g(x)$. Since there is a rational number between any two real numbers we can find $r in mathbb Q$ such that $f(x) >r >t-g(x)$. Can you finish the proof now?
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
$endgroup$
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
add a comment |
$begingroup$
Write $f(x)+g(x) >t$ as $f(x) >t-g(x)$. Since there is a rational number between any two real numbers we can find $r in mathbb Q$ such that $f(x) >r >t-g(x)$. Can you finish the proof now?
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
$endgroup$
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
add a comment |
$begingroup$
Write $f(x)+g(x) >t$ as $f(x) >t-g(x)$. Since there is a rational number between any two real numbers we can find $r in mathbb Q$ such that $f(x) >r >t-g(x)$. Can you finish the proof now?
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
$endgroup$
Write $f(x)+g(x) >t$ as $f(x) >t-g(x)$. Since there is a rational number between any two real numbers we can find $r in mathbb Q$ such that $f(x) >r >t-g(x)$. Can you finish the proof now?
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
answered Apr 8 at 6:38
Kavi Rama MurthyKavi Rama Murthy
74.4k53270
74.4k53270
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
add a comment |
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
$begingroup$
Gotcha. Thanks! Basically $leftf > t - g right = cup_r in mathbbQ leftf > r > t - g right = cup_r in mathbbQ leftf > rright cap leftr > t - g right$
$endgroup$
– nalzok
Apr 8 at 6:39
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%2f3179254%2fdecomposing-f-g-t%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
