Mixing
Having trouble following the logic of this proof
1
$begingroup$
I'm confused about
1) The highlighted portion
2) The logic of the proof thereafter. Thanks.
enter image description here
enter image description here
real-analysis proof-explanation
asked Feb 3 at 3:52
quant actuaryquant actuary
61
$endgroup$
add a comment |
1
$begingroup$
I'm confused about
1) The highlighted portion
2) The logic of the proof thereafter. Thanks.
enter image description here
enter image description here
real-analysis proof-explanation
asked Feb 3 at 3:52
quant actuaryquant actuary
61
$endgroup$
$begingroup$
Everyone here hates image links. Take the time to typeset your question correctly, together with your efforts and understanding of the problem, and you'll help people to help you. It's also good to have an actual question.
$endgroup$
– Randall
Feb 3 at 3:54
$begingroup$
Thanks, will do.
$endgroup$
– quant actuary
Feb 3 at 3:56
$begingroup$
People here are crazy helpful if the poster shows effort. It's great.
$endgroup$
– Randall
Feb 3 at 3:57
$begingroup$
Also, if you have two separate questions, make them two separate posts.
$endgroup$
– Randall
Feb 3 at 3:58
add a comment |
1
1
1
$begingroup$
I'm confused about
1) The highlighted portion
2) The logic of the proof thereafter. Thanks.
enter image description here
enter image description here
real-analysis proof-explanation
asked Feb 3 at 3:52
quant actuaryquant actuary
61
$endgroup$
I'm confused about
1) The highlighted portion
2) The logic of the proof thereafter. Thanks.
enter image description here
enter image description here
real-analysis proof-explanation
real-analysis proof-explanation
asked Feb 3 at 3:52
quant actuaryquant actuary
61
asked Feb 3 at 3:52
quant actuaryquant actuary
61
asked Feb 3 at 3:52
quant actuaryquant actuary
61
asked Feb 3 at 3:52
quant actuaryquant actuary
61
asked Feb 3 at 3:52
quant actuaryquant actuary
61
61
$begingroup$
Everyone here hates image links. Take the time to typeset your question correctly, together with your efforts and understanding of the problem, and you'll help people to help you. It's also good to have an actual question.
$endgroup$
– Randall
Feb 3 at 3:54
$begingroup$
Thanks, will do.
$endgroup$
– quant actuary
Feb 3 at 3:56
$begingroup$
People here are crazy helpful if the poster shows effort. It's great.
$endgroup$
– Randall
Feb 3 at 3:57
$begingroup$
Also, if you have two separate questions, make them two separate posts.
$endgroup$
– Randall
Feb 3 at 3:58
add a comment |
$begingroup$
Everyone here hates image links. Take the time to typeset your question correctly, together with your efforts and understanding of the problem, and you'll help people to help you. It's also good to have an actual question.
$endgroup$
– Randall
Feb 3 at 3:54
$begingroup$
Thanks, will do.
$endgroup$
– quant actuary
Feb 3 at 3:56
$begingroup$
People here are crazy helpful if the poster shows effort. It's great.
$endgroup$
– Randall
Feb 3 at 3:57
$begingroup$
Also, if you have two separate questions, make them two separate posts.
$endgroup$
– Randall
Feb 3 at 3:58
$begingroup$
Everyone here hates image links. Take the time to typeset your question correctly, together with your efforts and understanding of the problem, and you'll help people to help you. It's also good to have an actual question.
$endgroup$
– Randall
Feb 3 at 3:54
$begingroup$
Everyone here hates image links. Take the time to typeset your question correctly, together with your efforts and understanding of the problem, and you'll help people to help you. It's also good to have an actual question.
$endgroup$
– Randall
Feb 3 at 3:54
$begingroup$
Thanks, will do.
$endgroup$
– quant actuary
Feb 3 at 3:56
$begingroup$
Thanks, will do.
$endgroup$
– quant actuary
Feb 3 at 3:56
$begingroup$
People here are crazy helpful if the poster shows effort. It's great.
$endgroup$
– Randall
Feb 3 at 3:57
$begingroup$
People here are crazy helpful if the poster shows effort. It's great.
$endgroup$
– Randall
Feb 3 at 3:57
$begingroup$
Also, if you have two separate questions, make them two separate posts.
$endgroup$
– Randall
Feb 3 at 3:58
$begingroup$
Also, if you have two separate questions, make them two separate posts.
$endgroup$
– Randall
Feb 3 at 3:58
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
The reason why we could choose a bound of $mid x - 2mid$ is that the limit is a local feature. We could only consider the case where $x$ is near $2$.
How we choose $delta$ here is simple to consider the restriction that we mentioned earlier and to make sure the difference is less than $epsilon$.
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
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
});
}
});
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%2f3098149%2fhaving-trouble-following-the-logic-of-this-proof%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
1
$begingroup$
The reason why we could choose a bound of $mid x - 2mid$ is that the limit is a local feature. We could only consider the case where $x$ is near $2$.
How we choose $delta$ here is simple to consider the restriction that we mentioned earlier and to make sure the difference is less than $epsilon$.
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
add a comment |
1
$begingroup$
The reason why we could choose a bound of $mid x - 2mid$ is that the limit is a local feature. We could only consider the case where $x$ is near $2$.
How we choose $delta$ here is simple to consider the restriction that we mentioned earlier and to make sure the difference is less than $epsilon$.
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
add a comment |
1
1
1
$begingroup$
The reason why we could choose a bound of $mid x - 2mid$ is that the limit is a local feature. We could only consider the case where $x$ is near $2$.
How we choose $delta$ here is simple to consider the restriction that we mentioned earlier and to make sure the difference is less than $epsilon$.
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
The reason why we could choose a bound of $mid x - 2mid$ is that the limit is a local feature. We could only consider the case where $x$ is near $2$.
How we choose $delta$ here is simple to consider the restriction that we mentioned earlier and to make sure the difference is less than $epsilon$.
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
answered Feb 3 at 4:00
Alvis NordkovichAlvis Nordkovich
256110
256110
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
add a comment |
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
I'm not understanding your logic - they obtained abs(x-2) from what appears to be a simplification of the lhs numerator. I'm still confused as to how they did that simplication and the intution behind "to get an upper bound, we restrict ... "
$endgroup$
– quant actuary
Feb 3 at 4:10
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
$begingroup$
@quantactuary It is separating $mid x-2 mid$ so it could bound the coefficient of this term. Since we only need to consider where $x$ near 2, we could bound the coefficient by an interval containing 2. So it is easier to find a $delta$ that works.
$endgroup$
– Alvis Nordkovich
Feb 3 at 4:16
add a comment |
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%2f3098149%2fhaving-trouble-following-the-logic-of-this-proof%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
$begingroup$
Everyone here hates image links. Take the time to typeset your question correctly, together with your efforts and understanding of the problem, and you'll help people to help you. It's also good to have an actual question.
$endgroup$
– Randall
Feb 3 at 3:54
$begingroup$
Thanks, will do.
$endgroup$
– quant actuary
Feb 3 at 3:56
$begingroup$
People here are crazy helpful if the poster shows effort. It's great.
$endgroup$
– Randall
Feb 3 at 3:57
$begingroup$
Also, if you have two separate questions, make them two separate posts.
$endgroup$
– Randall
Feb 3 at 3:58