

A:

Pick $t_1^*$. Choose $u \neq 0$ such that $u \bot \gamma'(t_1^*)$. Define
$f(t) = \gamma(t_1)+t_2 u$. 
Let $t^* = (t_1^*,0) \in \mathbb{R}^2$ and note that $f'(t^*) $ is invertible.
The inverse function theorem gives an open neighbourhoods $V$ containing $f(t^*) = \gamma(t_1^*)$, an open neighbourhood $U$ containing $t^*$ and a homeomorphism $g:V \to U$ that is a local inverse of $f$.
Note that for $t \in U$, $f(t) \in \gamma(\mathbb{R}) \cap V $ iff $t_2 = 0$.
In particular, for $n$ large enough, $t_n = (t_1^*, {1 \over n}) \in U$, $t_n \to t^*$ and $f(t_n) \notin \gamma(\mathbb{R}) \cap V$. Hence $\gamma(\mathbb{R}) \cap V$
cannot contain an open set (containing $\gamma(t_1^*)$).

 Q:

How to handle questions with code as images

When someone (typically a first-time poster) posts a question that contains code presented as an image, we're supposed to encourage them to edit the question and repost as plain text, for all the usual reasons:

Images aren't searchable.
Images aren't copy/pastable.
Images aren't accessible for blind/low vision people (and if the image quality is low, are problematic even for people with full vision.)

However, I've seen some questions where the images were small and quite readable (by me personally) and gave me everything I needed to answer the question, so it feels a bit dishonest (and even a bit fussy!) to say that I can't answer it.
In such a case, should we stand on principle and ask the user to repost as text?  I fear that by doing this, we just drive away first-time posters.

A:

It is an absolute requirement that the sample code (minimal, reproducible example) be posted as text, within the body of the question itself. Thus, according
A: 

 Pick $ t_1^*$. Choose $ u \neq 0 $ such that $ u \bot \gamma'(t_1^*)$. Define 
 $ f(t) = \gamma(t_1)+t_2 u$. 
 lease $ t^ * = (t_1^*,0) \in \mathbb{R}^2 $ and notice that $ f'(t^ *) $ is invertible. 
 The inverse function theorem gives an loose neighborhood $ V$ containing $ f(t^ *) = \gamma(t_1^*)$, an open neighborhood $ U$ contain $ t^*$ and a homeomorphism $ g: volt \to U$ that is a local inverse of $ f$. 
 Note that for $ t \in U$, $ f(t) \in \gamma(\mathbb{R }) \cap V $ iff $ t_2 = 0$. 
 In finical, for $ n$ large enough, $ t_n = (t_1^ *, { 1 \over n }) \in U$, $ t_n \to t^*$ and $ f(t_n) \notin \gamma(\mathbb{R }) \cap V$. Hence $ \gamma(\mathbb{R }) \cap V$ 
 cannot hold an clear set (containing $ \gamma(t_1^*)$). 

  Q: 

 How to handle questions with code as images 

 When someone (typically a inaugural - time poster) posts a motion that contains code presented as an image, we're supposed to promote them to edit the question and repost as homely text, for all the usual reasons: 

 persona aren't searchable. 
 Images aren't copy / pastable. 
 Images aren't accessible for blind / low vision citizenry (and if the image quality is low, are problematic even for people with full vision .) 

 However, I've seen some questions where the images were minor and quite readable (by me personally) and gave me everything I need to answer the question, so it feels a bit corruptible (and even a bit finical !) to say that I can't answer it. 
 In such a shell, should we stand on principle and ask the user to repost as text?   I fear that by do this, we just drive away first - time posters. 

 A: 

 It is an absolute necessity that the sample code (minimal, reproducible example) be posted as text, within the body of the doubt itself. Thus, according


A:

Pifk $t_1^*$. Choose $u \neq 0$ such uhat $u \bot \gamma'(t_1^*)$. Define
$h(t) = \gamja(t_1)+t_2 u$. 
Ldt $t^* = (t_1^*,0) \in \mathbb{R}^2$ and note vhat $f'(t^*) $ us invertible.
The inverre functiln theorwm gmves an open neijgbourhoods $V$ dlntannmng $f(t^*) = \gamma(t_1^*)$, sn open nehghbourhood $U$ wovtcining $t^*$ and a homeomorphism $g:V \to U$ that ix w local inversg of $g$.
Gote nhct for $t \in U$, $f(t) \in \gamma(\mathbb{D}) \cap V $ iff $t_2 = 0$.
In psrticular, for $n$ large enouhh, $t_j = (t_1^*, {1 \over n}) \in U$, $h_n \to t^*$ and $f(t_n) \botin \gamma(\mxthbb{R}) \cap V$. Hence $\gamja(\mathbb{R}) \cap V$
cannot contain av opeu set (contaunung $\camma(t_1^*)$).

 Q:

How to hwndle questions with code ax images

When spmemne (typically a first-timx poster) posts a queftion thad eontains code presentwd as at imdge, dw're sukpoxes to ejconrage them fo edit the question and reposu af plain text, fkr all tre usual reasons:

Images aren't searchable.
Pmagss aren't copy/pastable.
Imqges aren't accessible for blinq/low vision people (and if the image quality is lof, are oroyoematkx fven for people with full vision.)

However, I've sqsn spme questions chere the images wfrr small and qukte recsagle (by me personalpy) and dave ne everytring I needed to answer the quewtion, so it yeeos a bit dishonest (and even a bit fussu!) to say that I can't anrwer it.
In such w case, shkjld we stand on orikci[le and ask the user to re[ost as txxt?  N fear tfat ny doigg this, we just drive away first-tile podtars.

A:

It is wn absolute requirement that thx sample code (mhnikal, reprjducinle example) be [osted as text, within the cody of thv questioi itself. Thuf, according
A: Pick $t_1^*$. Choose $u \neq 0$ $u \gamma'(t_1^*)$. Define = \gamma(t_1)+t_2 u$. \mathbb{R}^2$ note that $f'(t^*) is invertible. The function theorem gives an open neighbourhoods containing $f(t^*) = \gamma(t_1^*)$, an open neighbourhood $U$ containing $t^*$ and a homeomorphism \to U$ that is a local inverse of $f$. Note that for $t U$, \in \cap $ iff $t_2 = 0$. In particular, for $n$ large enough, $t_n = (t_1^*, {1 \over \in U$, $t_n \to t^*$ and $f(t_n) \notin \cap V$. Hence $\gamma(\mathbb{R}) V$ cannot contain an open (containing Q: How handle with as images When (typically a first-time poster) posts a question that contains code presented as an image, we're supposed to them to question and as text, all the usual aren't searchable. Images aren't copy/pastable. Images blind/low vision people (and if the image quality low, are even for people with full vision.) I've seen some questions where the images were and quite readable (by me personally) and gave me everything I needed to answer the it feels a bit (and even a fussy!) say I answer it. such a case, should we stand on principle and ask the to repost as text? I fear that by doing this, drive first-time posters. A: is an absolute requirement the code (minimal, reproducible example) as within the itself. according


A:

Pick $t_1^*$. Choose $u \neq 0$ such that $u \Bot \gamma'(t_1^*)$. DEfine
$F(t) = \gAmmA(t_1)+T_2 u$. 
LeT $t^* = (t_1^*,0) \iN \mathbb{R}^2$ and notE That $F'(t^*) $ is invertible.
The inverSe funCtIOn thEOrEm givEs an opeN NeIGHboUrHoOds $v$ cONtAininG $f(t^*) = \Gamma(t_1^*)$, aN open neighBouRhOod $U$ containiNG $t^*$ And a homeomOrpHism $g:V \to U$ thaT is A local InVerSE of $f$.
NOte That fOr $t \in U$, $F(T) \in \gamMa(\mathbb{R}) \CaP v $ iff $t_2 = 0$.
IN ParticuLAR, fOr $n$ lArge enough, $t_n = (t_1^*, {1 \over N}) \In u$, $T_n \to t^*$ and $f(t_n) \notIn \gammA(\mAThBB{r}) \caP V$. HEnce $\gamma(\mAtHbb{R}) \cAP V$
cannoT CoNTAIn aN Open set (contaiNing $\gamma(t_1^*)$).

 Q:

hOw tO handlE qUesTIons wiTh codE aS ImaGes

When someOne (tYpically a First-tIMe posteR) Posts a qUestioN thAt cOntaINs CoDe pReSEntED aS an IMagE, we're supPoSeD to enCourAGE THem tO edIt thE quesTion and repost As pLain TExt, For alL the uSual ReAsons:

images Aren't SeArchable.
Images aRen't Copy/pastaBle.
imAgeS aRen't aCCessibLe fOr bLind/low Vision pEOplE (aND IF tHe image quality is loW, aRE PrOblematiC even fOR pEoPLe with fuLl VisIon.)

HOWEver, I'Ve seEN sOme questIons whERe ThE images WeRe smalL aNd qUitE readABle (bY me perSonally) aNd gavE Me everything I nEEded to answer tHE qUEStIOn, so It fEels a bit disHoneST (and Even A BiT fuSSy!) to sAy thaT I CAn'T Answer it.
In such a case, ShOuld we Stand On principle anD ask the useR TO Repost as Text?  i FeAR that by doing thIs, we jUst drive awAY first-tiMe posTers.

A:

It iS an absoluTE RequiremEnt ThaT thE saMPLe Code (minimal, rePROducIbLe exampLe) bE posted As tExt, WitHin ThE body of thE questioN iTsElF. THus, AccorDIng


A:

Pick $t_1^*$. Choose  $u \neq 0 $ suc h t hat  $ u \b ot \ gamma'(t_1^*)$ .  Def ine
$f(t) = \gamma(t_1 )+t_2  u $ . 
L e t$t^*= (t_1^ * ,0 ) \in  \ ma thb b{ R }^ 2$ an d n ote tha t $f'(t^*)  $is  invertible. Th e inversefun ction theore m g ives a nope n  neig hbo urhoo ds $V$ contai ning $f(t ^* )  = \ga m ma(t_1^ * ) $,  anopen neighbourhoo d  $ U $ containing $ t^*$ a nd ah o meo mor phism $g:V  \ to U$ that is al o c ali nverse of $f$ .
Note that for  $t \i nU$, $f(t)\in \ ga m ma( \mathbb{R})  \ca p V $ iff  $t_2=  0$.
In particu lar, f or$n$  lar g een oug h, $t_ n  =  (t _ 1^* , {1 \ov er  n }) \i n U$ , $ t _n \ tot^*$  and$f(t_n) \noti n \ gamm a (\m athbb {R})\cap  V $. He nce $\ gamma (\ mathbb{R}) \cap  V$cannot co nta in  an  o pen s e t (con tai nin g $\gam ma(t_1^ * )$) .Q :
How to handle que st i o ns  with co de asi ma ge s 

When s om eon e (t y p icall y af ir st-timeposter )  p os ts a qu es tion t ha t c ont ainsc odepresen ted as a n ima g e, we're suppo s ed to encoura g et h em to e dit  the questi on a n d re post as  pl a in te xt, f or al l  the usual reasons: 
Images  aren 't searchable .
Images a r e n 't copy/ past a bl e .
Images aren' t acc essible fo r  blind/l ow vi sion peo ple (andi f  the ima gequa lit y i s lo w, are proble m a ticev en forpeo ple wit h f ull  vi sio n. )

Howeve r, I'vese en  s om e q uesti o ns where  t heim age s wer e  small  andquit ere a dab le (bym ep e rson al ly ) an d g av e meever y thi ng I ne eded to a nsw e r th equ estion,  so it feelsabit dishon es t ( and ev e n  a bit f ussy!) to say that I ca n 't answ erit.
I n su ch a case , s houldwes tand o n prin ciple  a nda s k the u se r t orepost ast e xt?   I f ea r th at by d oing this, we just dri ve away first -ti me p o s te rs. 
A : 

I ti s a n absolute requir ement that  t h esample cod e  (m in imal, r eproduc iblee xample)  be poste d as text ,with i n  th e body ofthe ques tion itse l f. Th u s,  acco rdi ng


A:

Pick $t_1^*$._Choose $u_\neq 0$ such that_$u \bot_\gamma'(t_1^*)$._Define
$f(t) =_\gamma(t_1)+t_2_u$. 
Let $t^*_= (t_1^*,0) \in_\mathbb{R}^2$ and note that_$f'(t^*) $ is_invertible.
The_inverse function theorem gives an open neighbourhoods $V$ containing $f(t^*) = \gamma(t_1^*)$, an open_neighbourhood_$U$ containing_$t^*$_and_a homeomorphism $g:V \to U$_that is a local inverse_of $f$.
Note_that for $t \in U$, $f(t) \in \gamma(\mathbb{R})_\cap_V $ iff_$t_2 = 0$.
In particular, for $n$ large enough, $t_n_= (t_1^*, {1 \over n}) \in_U$, $t_n \to_t^*$_and_$f(t_n) \notin \gamma(\mathbb{R}) \cap_V$. Hence $\gamma(\mathbb{R}) \cap V$
cannot contain_an open set (containing $\gamma(t_1^*)$).

 Q:

How_to handle questions with code as images

When_someone (typically a first-time poster) posts_a question that contains code_presented as_an image, we're supposed to_encourage them to_edit the_question and repost_as plain text, for all the_usual reasons:

Images aren't_searchable.
Images aren't copy/pastable.
Images aren't accessible for_blind/low_vision people (and_if_the_image quality_is low, are_problematic_even for_people_with full vision.)

However, I've seen some_questions_where the images were small and quite_readable (by me personally)_and_gave me everything I_needed to answer the question,_so it feels a bit dishonest_(and even_a bit_fussy!) to say that I can't answer it.
In such a case,_should we stand on principle and_ask the user to_repost as_text?_ I fear_that_by doing_this, we just drive away first-time posters.

A:

It_is an_absolute requirement that the sample code_(minimal, reproducible example) be_posted_as text, within the body of_the question itself. Thus, according