Let $f_n_ninmathbbN$ a Cauchy sequence in $C[0,1]$. then $f_n(x_0)_ninmathbbN$ is Cauchy

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












Let $f_n_ninmathbbN$ a Cauchy sequence in $C[0,1]$. Prove for each $x_0in[0,1]$ the sequence $f_n(x_0)_ninmathbbN$ is Cauchy in $mathbbR$



My work



Let $epsilon >0$

As $f_n_ninmathbbN$ then exists $NinmathbbN$ sucht that if $n,mgeq N$ then $d(f_n,f_m)<epsilon$



Here I'm stuck. Can someone help me?




general-topology




share|cite|improve this question

















  • 2




    Use the definition of $d(f_n,f_m)$. What does $d(f_n,f_m)<varepsilon$ mean in terms of the definition?
    – Lorenzo Quarisa
    Jul 15 at 20:21











  • @LorenzoQuarisa $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:27














up vote
0
down vote

favorite












Let $f_n_ninmathbbN$ a Cauchy sequence in $C[0,1]$. Prove for each $x_0in[0,1]$ the sequence $f_n(x_0)_ninmathbbN$ is Cauchy in $mathbbR$



My work



Let $epsilon >0$

As $f_n_ninmathbbN$ then exists $NinmathbbN$ sucht that if $n,mgeq N$ then $d(f_n,f_m)<epsilon$



Here I'm stuck. Can someone help me?




general-topology




share|cite|improve this question

















  • 2




    Use the definition of $d(f_n,f_m)$. What does $d(f_n,f_m)<varepsilon$ mean in terms of the definition?
    – Lorenzo Quarisa
    Jul 15 at 20:21











  • @LorenzoQuarisa $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:27












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let $f_n_ninmathbbN$ a Cauchy sequence in $C[0,1]$. Prove for each $x_0in[0,1]$ the sequence $f_n(x_0)_ninmathbbN$ is Cauchy in $mathbbR$



My work



Let $epsilon >0$

As $f_n_ninmathbbN$ then exists $NinmathbbN$ sucht that if $n,mgeq N$ then $d(f_n,f_m)<epsilon$



Here I'm stuck. Can someone help me?




general-topology




share|cite|improve this question













Let $f_n_ninmathbbN$ a Cauchy sequence in $C[0,1]$. Prove for each $x_0in[0,1]$ the sequence $f_n(x_0)_ninmathbbN$ is Cauchy in $mathbbR$



My work



Let $epsilon >0$

As $f_n_ninmathbbN$ then exists $NinmathbbN$ sucht that if $n,mgeq N$ then $d(f_n,f_m)<epsilon$



Here I'm stuck. Can someone help me?





general-topology





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 15 at 20:20









Bernard

110k635103




110k635103









asked Jul 15 at 20:19









Bvss12

1,609516




1,609516







  • 2




    Use the definition of $d(f_n,f_m)$. What does $d(f_n,f_m)<varepsilon$ mean in terms of the definition?
    – Lorenzo Quarisa
    Jul 15 at 20:21











  • @LorenzoQuarisa $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:27












  • 2




    Use the definition of $d(f_n,f_m)$. What does $d(f_n,f_m)<varepsilon$ mean in terms of the definition?
    – Lorenzo Quarisa
    Jul 15 at 20:21











  • @LorenzoQuarisa $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:27







2




2




Use the definition of $d(f_n,f_m)$. What does $d(f_n,f_m)<varepsilon$ mean in terms of the definition?
– Lorenzo Quarisa
Jul 15 at 20:21





Use the definition of $d(f_n,f_m)$. What does $d(f_n,f_m)<varepsilon$ mean in terms of the definition?
– Lorenzo Quarisa
Jul 15 at 20:21













@LorenzoQuarisa $d(f,g)=sup$ in my definition.
– Bvss12
Jul 15 at 20:27




@LorenzoQuarisa $d(f,g)=sup$ in my definition.
– Bvss12
Jul 15 at 20:27










1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










Hint:



How is the distance $d(f, g)$ in the vector space $mathcal C[0,1]$ defined?






share|cite|improve this answer





















  • $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:25











  • So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
    – Bernard
    Jul 15 at 20:31











  • $|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
    – Bvss12
    Jul 15 at 20:32











  • Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
    – Bernard
    Jul 15 at 20:39











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',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);








 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2852813%2flet-f-n-n-in-mathbbn-a-cauchy-sequence-in-c0-1-then-f-nx-0%23new-answer', 'question_page');

);

Post as a guest

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










Hint:



How is the distance $d(f, g)$ in the vector space $mathcal C[0,1]$ defined?






share|cite|improve this answer





















  • $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:25











  • So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
    – Bernard
    Jul 15 at 20:31











  • $|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
    – Bvss12
    Jul 15 at 20:32











  • Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
    – Bernard
    Jul 15 at 20:39















up vote
1
down vote



accepted










Hint:



How is the distance $d(f, g)$ in the vector space $mathcal C[0,1]$ defined?






share|cite|improve this answer





















  • $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:25











  • So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
    – Bernard
    Jul 15 at 20:31











  • $|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
    – Bvss12
    Jul 15 at 20:32











  • Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
    – Bernard
    Jul 15 at 20:39













up vote
1
down vote



accepted







up vote
1
down vote



accepted






Hint:



How is the distance $d(f, g)$ in the vector space $mathcal C[0,1]$ defined?






share|cite|improve this answer













Hint:



How is the distance $d(f, g)$ in the vector space $mathcal C[0,1]$ defined?







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 15 at 20:24









Bernard

110k635103




110k635103











  • $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:25











  • So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
    – Bernard
    Jul 15 at 20:31











  • $|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
    – Bvss12
    Jul 15 at 20:32











  • Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
    – Bernard
    Jul 15 at 20:39

















  • $d(f,g)=sup$ in my definition.
    – Bvss12
    Jul 15 at 20:25











  • So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
    – Bernard
    Jul 15 at 20:31











  • $|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
    – Bvss12
    Jul 15 at 20:32











  • Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
    – Bernard
    Jul 15 at 20:39
















$d(f,g)=sup$ in my definition.
– Bvss12
Jul 15 at 20:25





$d(f,g)=sup$ in my definition.
– Bvss12
Jul 15 at 20:25













So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
– Bernard
Jul 15 at 20:31





So for each $x in [0,1]$, one has $;|f(x)-g(x)|le d(f,g)$, right?
– Bernard
Jul 15 at 20:31













$|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
– Bvss12
Jul 15 at 20:32





$|f_n(x_0)-f_m(x_0)|<supf_n(x)-f_m(x)<epsilon$ then $f_n(x_0)$ is cauchy in $mathbbR$ is correct this Bernard? Thanks for help me (:
– Bvss12
Jul 15 at 20:32













Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
– Bernard
Jul 15 at 20:39





Quite cotrect.. Unrelated: for proper min, max, &c., in maths formulæ, type them code as min or max.
– Bernard
Jul 15 at 20:39













 

draft saved


draft discarded


























 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2852813%2flet-f-n-n-in-mathbbn-a-cauchy-sequence-in-c0-1-then-f-nx-0%23new-answer', 'question_page');

);

Post as a guest
































































Comments

Post a Comment

Popular posts from this blog

What is the equation of a 3D cone with generalised tilt?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
Read more

Color the edges and diagonals of a regular polygon

Image
Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
Read more

Relationship between determinant of matrix and determinant of adjoint?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
Read more