Fdtxjr

Is it possible to put a rectangle as background in the author section?

Why did the EU agree to delay the Brexit deadline?

Can I sign legal documents with a smiley face?

Problem with TransformedDistribution

Store Credit Card Information in Password Manager?

Travelling outside the UK without a passport

Is it better practice to read straight from sheet music rather than memorize it?

Multiplicative persistence

"Spoil" vs "Ruin"

What is this called? Old film camera viewer?

What does chmod -u do?

What was this official D&D 3.5e Lovecraft-flavored rulebook?

Offered money to buy a house, seller is asking for more to cover gap between their listing and mortgage owed

Aragorn's "guise" in the Orthanc Stone

C++ debug/print custom type with GDB : the case of nlohmann json library

Biological Blimps: Propulsion

What is Cash Advance APR?

Lowest total scrabble score

Is there any references on the tensor product of presentable (1-)categories?

What should you do if you miss a job interview (deliberately)?

Why electric field inside a cavity of a non-conducting sphere not zero?

What does "Scientists rise up against statistical significance" mean? (Comment in Nature)

Closed-form expression for certain product

Should I outline or discovery write my stories?

How can I properly define $R$ and $R^2$?

Sum of product of (3i - 2)/(5i)Show $f=g$ for all reals given $f=g$ for all rationals ( epsilon-delta continuity)Let $a_n$ be a sequence with limit $alpha$, and define $b_n=a_n+1$ where $nin mathbbN$. Show that $b_nrightarrow alpha$.Showing a point is a limit point of a setContinuity of a function over the open intervalShowing $|f |_2$ isn't equivalent to $| f|_infty$On constructing the definition of differentiationA fixed point theorem for continuous and increasing function on $[0,1]$Intro to Real Analysis: Riemann IntegralsProve that $f'(x) > frac f(x)x$ for a continuous, differentiable $f(x)$

2

$begingroup$

I am looking for a definition of $R$ and $R^2$ to use in a report I'm writing.

I have the following line where I am struggling to figure out what $R$ and consequently $R^2$ means:

$f$ and $f_x$ are continuous in the rectangle:
$R = (x,t):aleq x leq b, c leq t leq d$

Any help would be greatly appreciated. I'm guessing $R$ is a region of 2 dimension as a starting point?

real-analysis definition

share|cite|improve this question

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

$endgroup$

add a comment | 

2

$begingroup$

I am looking for a definition of $R$ and $R^2$ to use in a report I'm writing.

I have the following line where I am struggling to figure out what $R$ and consequently $R^2$ means:

$f$ and $f_x$ are continuous in the rectangle:
$R = (x,t):aleq x leq b, c leq t leq d$

Any help would be greatly appreciated. I'm guessing $R$ is a region of 2 dimension as a starting point?

real-analysis definition

share|cite|improve this question

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

$endgroup$

add a comment | 

$begingroup$

I am looking for a definition of $R$ and $R^2$ to use in a report I'm writing.

I have the following line where I am struggling to figure out what $R$ and consequently $R^2$ means:

$f$ and $f_x$ are continuous in the rectangle:
$R = (x,t):aleq x leq b, c leq t leq d$

Any help would be greatly appreciated. I'm guessing $R$ is a region of 2 dimension as a starting point?

real-analysis definition

share|cite|improve this question

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

$endgroup$

share|cite|improve this question

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

share|cite|improve this question

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

asked Mar 15 at 16:46

KeighleyiteKeighleyite

788

2 Answers
2

active

oldest

votes

2

$begingroup$

$R$ is a rectangle in the plane $mathbbR^2$. Its corners are $(a,c)$ and $(b,d)$. Note that for a point $(x,y)$ to be in a rectangle, it must be between any two opposite corners, which is the case if and only if both coordinates (i.e., both $x$ and $y$) lie between the respective coordinates of the corners. This is exactly how $R$ is defined.

share|cite|improve this answer

answered Mar 15 at 17:18

NicolasNicolas

1467

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $R^2$ could also be the box defined by n-tuples in 3 space of (a,c,a),(a,d,a),(a,c,b),(b,c,a)
  $endgroup$
  – Roddy MacPhee
  Mar 16 at 0:34
  

  
  
  
  

add a comment | 

1

$begingroup$

Nicolas, gave you the answer, if you wanted to talk about the Cartesian product of the reals with the reals (usually called the Cartesian plane in this set analysis) for $R^2$. Usually we use the notation mathbbR which produces the double struck $mathbbR$ for the reals. In this case, I believe the definition of $R^2$ is the Cartesian product of the the set R with itself. R appears to be a bounded shape, called a rectangle. The set notation definition for $R^2$ could be as follows:$$R^2 = (x_1,t_1,x_2,t_2):aleq x_1,x_2leq b ; cleq t_1,t_2 leq d$$

This new shape, is called a box (it is only a cube if d-c=b-a)

share|cite|improve this answer

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117

$endgroup$

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
);



);

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

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3149523%2fhow-can-i-properly-define-r-and-r2%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

2

$begingroup$

$R$ is a rectangle in the plane $mathbbR^2$. Its corners are $(a,c)$ and $(b,d)$. Note that for a point $(x,y)$ to be in a rectangle, it must be between any two opposite corners, which is the case if and only if both coordinates (i.e., both $x$ and $y$) lie between the respective coordinates of the corners. This is exactly how $R$ is defined.

share|cite|improve this answer

answered Mar 15 at 17:18

NicolasNicolas

1467

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $R^2$ could also be the box defined by n-tuples in 3 space of (a,c,a),(a,d,a),(a,c,b),(b,c,a)
  $endgroup$
  – Roddy MacPhee
  Mar 16 at 0:34
  

  
  
  
  

add a comment | 

2

$begingroup$

$R$ is a rectangle in the plane $mathbbR^2$. Its corners are $(a,c)$ and $(b,d)$. Note that for a point $(x,y)$ to be in a rectangle, it must be between any two opposite corners, which is the case if and only if both coordinates (i.e., both $x$ and $y$) lie between the respective coordinates of the corners. This is exactly how $R$ is defined.

share|cite|improve this answer

answered Mar 15 at 17:18

NicolasNicolas

1467

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $R^2$ could also be the box defined by n-tuples in 3 space of (a,c,a),(a,d,a),(a,c,b),(b,c,a)
  $endgroup$
  – Roddy MacPhee
  Mar 16 at 0:34
  

  
  
  
  

add a comment | 

$begingroup$

$R$ is a rectangle in the plane $mathbbR^2$. Its corners are $(a,c)$ and $(b,d)$. Note that for a point $(x,y)$ to be in a rectangle, it must be between any two opposite corners, which is the case if and only if both coordinates (i.e., both $x$ and $y$) lie between the respective coordinates of the corners. This is exactly how $R$ is defined.

share|cite|improve this answer

answered Mar 15 at 17:18

NicolasNicolas

1467

$endgroup$

share|cite|improve this answer

answered Mar 15 at 17:18

NicolasNicolas

1467

answered Mar 15 at 17:18

NicolasNicolas

1467

answered Mar 15 at 17:18

NicolasNicolas

1467

1

$begingroup$

Nicolas, gave you the answer, if you wanted to talk about the Cartesian product of the reals with the reals (usually called the Cartesian plane in this set analysis) for $R^2$. Usually we use the notation mathbbR which produces the double struck $mathbbR$ for the reals. In this case, I believe the definition of $R^2$ is the Cartesian product of the the set R with itself. R appears to be a bounded shape, called a rectangle. The set notation definition for $R^2$ could be as follows:$$R^2 = (x_1,t_1,x_2,t_2):aleq x_1,x_2leq b ; cleq t_1,t_2 leq d$$

This new shape, is called a box (it is only a cube if d-c=b-a)

share|cite|improve this answer

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117

$endgroup$

add a comment | 

1

$begingroup$

Nicolas, gave you the answer, if you wanted to talk about the Cartesian product of the reals with the reals (usually called the Cartesian plane in this set analysis) for $R^2$. Usually we use the notation mathbbR which produces the double struck $mathbbR$ for the reals. In this case, I believe the definition of $R^2$ is the Cartesian product of the the set R with itself. R appears to be a bounded shape, called a rectangle. The set notation definition for $R^2$ could be as follows:$$R^2 = (x_1,t_1,x_2,t_2):aleq x_1,x_2leq b ; cleq t_1,t_2 leq d$$

This new shape, is called a box (it is only a cube if d-c=b-a)

share|cite|improve this answer

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117

$endgroup$

add a comment | 

$begingroup$

Nicolas, gave you the answer, if you wanted to talk about the Cartesian product of the reals with the reals (usually called the Cartesian plane in this set analysis) for $R^2$. Usually we use the notation mathbbR which produces the double struck $mathbbR$ for the reals. In this case, I believe the definition of $R^2$ is the Cartesian product of the the set R with itself. R appears to be a bounded shape, called a rectangle. The set notation definition for $R^2$ could be as follows:$$R^2 = (x_1,t_1,x_2,t_2):aleq x_1,x_2leq b ; cleq t_1,t_2 leq d$$

This new shape, is called a box (it is only a cube if d-c=b-a)

share|cite|improve this answer

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117

$endgroup$

share|cite|improve this answer

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117

answered Mar 16 at 1:13

Roddy MacPheeRoddy MacPhee

527117