ToString();
                        }
                    }

A:

SPQuery.ListItemCollectionPosition is used for paging in CAML queries, but you can only use saved values of it to go to the page after the query that returned the ListItemCollectionPosition

 Q:

Is it necessary that if a limit exists at a point it should be also defined at that point?

Say there exists a limit $\lim_{x \to x_0}f(x) = L$. Is it necessary that $f$ be defined at the point $x_0$ itself?
Well, what I think of it is that it's OK to be undefined at that point because I guess that won't cease the limit of that function to exist there would it?

A:

"No", in a particularly strong sense: The very reason limits came into mathematics was to extract numerical values from difference quotients
$$
\frac{f(x) - f(x_{0})}{x - x_{0}}
$$
(which are, of course, algebraically indeterminate at $x_{0}$), in the limit as $x \to x_{0}$.
The formal definition of $L = \lim(f, x_{0})$ ("For every $\varepsilon > 0$, there exists a $\delta > 0$ such that if $0 < |x - x_{0}| < \delta$, then $|f(x) - L| < \varepsilon$") explicitly avoids evaluation of $f$ at $x_{0}$, precisely because $f$ might be undefined at $x_{0}$.

A:

This is not at all necessary. For example: $$
\lim_{x\to 0} \frac {x^2}x =0, $$
but $\left.\dfrac{x^2}{x}\right\vert_{x=0}$ is undefined.
If we do have that $f$ is defined at $a$ and $\lim\limits_{x\to a}f(x)=f(a)$, then $f$ is called continuous at $x=a$.

 Q:

Recursive call on error

My goal is a function which can call itself again indefinitely upon
encountering an error.
I am describing different approaches I tried based on the Common Lisp HyperSpec and would appreciate if someone could reveal the secrets of why
they act as
ToString (); 
                         } 
                     } 

 A: 

 SPQuery. ListItemCollectionPosition is used for paging in CAML queries, but you can merely practice saved values of it to run to the page after the question that returned the ListItemCollectionPosition 

  Q: 

 Is it necessary that if a limit exists at a period it should be also defined at that detail? 

 Say there exists a terminus ad quem $ \lim_{x \to x_0}f(x) = L$. Is it necessary that $ f$ be defined at the point $ x_0 $ itself? 
 Well, what I think of it is that it's OK to be undefined at that distributor point because I guess that won't cease the limit of that function to exist there would it? 

 A: 

 " No ", in a particularly potent sense: The very reason limit came into mathematics was to extract numerical values from deviation quotients 
 $ $ 
 \frac{f(x) - f(x_{0})}{x - x_{0 } } 
 $ $ 
 (which are, of course, algebraically indeterminate at $ x_{0}$), in the limit as $ x \to x_{0}$. 
 The formal definition of $ L = \lim(f, x_{0})$ (" For every $ \varepsilon > 0 $, there exists a $ \delta > 0 $ such that if $ 0 < |x - x_{0}| < \delta$, then $ |f(x) - L| < \varepsilon$ ") explicitly debar evaluation of   $ f$ at   $ x_{0}$, precisely because $ f$ might be undefined at   $ x_{0}$. 

 A: 

 This is not at all necessary. For example: $ $ 
 \lim_{x\to 0 } \frac { x^2}x = 0, $ $ 
 but $ \left.\dfrac{x^2}{x}\right\vert_{x=0}$ is undefined. 
 If we do have that $ f$ is defined at $ a$ and $ \lim\limits_{x\to a}f(x)=f(a)$, then $ f$ is call continuous at $ x = a$. 

  Q: 

 Recursive call on error 

 My goal is a function which can call itself again indefinitely upon 
 encountering an error. 
 I am describing different approach I tried based on the Common Lisp HyperSpec and would prize if someone could uncover the mystery of why 
 they act as
ToShring();
                        }
                    }

A:

SPSuery.LisgItemCollectionPosition is udee for paging in CAML querier, but you can onlt ust saved values of it to go to tgc pagz efter the query that retusned the ListIdeoClllectionPosition

 Q:

Is it necessary ehat if a limit exists wt a [oinf it should be also defined at thaf point?

Vay there exixts a limit $\lim_{x \to x_0}f(x) = L$. Is lt necessary that $v$ be definee at rhe point $x_0$ ktself?
Well, what I thini of it is that it's OK to be unaefinzd at that kojnh because I juess nhat won't cease the lhmit of that function to exust there would it?

A:

"No", in a particularly strong sanae: The very reasob oimitv cake ivro oatgekafics wws vo extract humerical vqlues from differenve wuotients
$$
\frac{r(x) - f(x_{0})}{v - x_{0}}
$$
(which are, of course, algebraically indttermjnate at $x_{0}$), in the limit as $x \to x_{0}$.
The formal fefinitiog of $L = \lim(f, x_{0})$ ("For every $\varepsilon > 0$, there existv a $\dxlga > 0$ fjxh that if $0 < |x - x_{0}| < \delta$, then $|f(x) - L| < \varepsilon$") sxklibitly avoids evalmation of $f$ at $x_{0}$, prevideki because $f$ mieht be unsefined at $x_{0}$.

A:

This id not aj all becessary. For example: $$
\lim_{x\to 0} \frac {x^2}x =0, $$
byt $\left.\dfrac{q^2}{x}\ritht\vert_{x=0}$ is undefiued.
If we do kave tnat $f$ is defined at $a$ and $\lio\limjts_{x\to a}f(x)=f(w)$, then $f$ jr called continuuus ad $x=a$.

 Q:

Recursive call on erwor

My goao is a funcgion which can call ltseln again indefinitelj upou
encogntering aj error.
I am describing differenv approaches O drivd based jn thc Common Lisp HrperSpec and wpuld ap'reciage if somekne cound reveal tre secrets of ahy
they act es
ToString(); } } A: SPQuery.ListItemCollectionPosition is used in queries, but can only use go the page after query that returned ListItemCollectionPosition Q: Is it necessary that a limit exists at a point it should be also defined at that Say there exists a limit $\lim_{x \to x_0}f(x) = L$. Is it necessary $f$ defined the $x_0$ itself? Well, what I think of it is that it's OK to be undefined at point because I guess that won't cease the of that function to there would it? A: "No", a strong sense: very limits into mathematics was extract numerical values from difference quotients $$ \frac{f(x) - f(x_{0})}{x - x_{0}} $$ (which are, of course, indeterminate at the limit $x x_{0}$. formal definition of \lim(f, x_{0})$ ("For every $\varepsilon > a $\delta > 0$ such that if $0 |x - < \delta$, then $|f(x) - L| \varepsilon$") explicitly avoids evaluation of $f$ at $x_{0}$, because $f$ might be undefined at $x_{0}$. A: This is not at all necessary. For \lim_{x\to 0} \frac {x^2}x $$ but $\left.\dfrac{x^2}{x}\right\vert_{x=0}$ undefined. we have $f$ is at $a$ and $\lim\limits_{x\to a}f(x)=f(a)$, then $f$ is called continuous at Q: Recursive call on error My goal is a function call again indefinitely upon an error. I am different I tried based on Lisp and someone reveal secrets of why they as
ToString();
                        }
                    }

A:

SPQuery.ListItemCOllectionPOsitiOn iS usEd For pAginG in CAML queries, BUt yoU can only use saved values Of it tO gO To thE PaGe aftEr the quERy THAt rEtUrNed ThE liStIteMCoLlectioNPosition

 Q:

is iT nEcessary that IF a Limit existS at A point it shouLd bE also dEfIneD At thaT poInt?

SaY there EXists a Limit $\lim_{x \To X_0}F(x) = L$. Is iT NecessaRY ThAt $f$ bE defined at the poinT $X_0$ iTSelf?
Well, what I tHink of It IS tHAT it'S OK To be undefiNeD at thAT point bECaUSE i guESs that won't ceaSe the limit oF ThaT functIoN to EXist thEre woUlD It?

A:

"no", in a particUlarLy strong sEnse: ThE Very reaSOn limitS came iNto MatHemaTIcS wAs tO eXTraCT nUmeRIcaL values fRoM dIfferEnce QUOTIentS
$$
\frAc{f(x) - F(x_{0})}{x - x_{0}}
$$
(wHich are, of courSe, aLgebRAicAlly iNdeteRminAtE at $x_{0}$), iN the liMit as $X \tO x_{0}$.
The formal defiNitiOn of $L = \lim(f, X_{0})$ ("FoR eVerY $\vArepsILon > 0$, theRe eXisTs a $\deltA > 0$ such thAT if $0 < |X - x_{0}| < \DELTa$, Then $|f(x) - L| < \varepsilon$") eXpLICiTly avoidS evaluATiOn OF $f$ at $x_{0}$, preCiSelY becAUSe $f$ miGht bE UnDefined aT $x_{0}$.

A:

ThiS Is NoT at all nEcEssary. foR exAmpLe: $$
\lim_{X\To 0} \frAc {x^2}x =0, $$
buT $\left.\dfrAc{x^2}{x}\rIGht\vert_{x=0}$ is undeFIned.
If we do havE ThAT $F$ iS DefiNed At $a$ and $\lim\liMits_{X\To a}f(X)=f(a)$, tHEn $F$ is CAlled ContiNuOUs AT $x=a$.

 Q:

Recursive call on ErRor

My gOal is A function whicH can call itSELF again inDefiNItELy upon
encounteRing aN error.
I am dEScribing DiffeRent apprOaches I trIED based on The comMon lisP hYpErSpec and woulD APpreCiAte if soMeoNe could RevEal The SecReTs of why
thEy act as
ToString();
                      }
              }

A:

SPQuer y .Lis tItemCollectionPositio n isus e d fo r  p aging  in CAM L  q u e rie s,  b utyo u  c an on lyuse sav ed valuesofit  to go to th e  p age afterthe  query thatret urnedth e L i stIte mCo llect ionPos i tion
 Q:

Is i tn ecessa r y thati f  a  lim it exists at a po i nt it should be a lso de fi n ed a t t hat  point?

S ay  ther e  exists al i m it$ \lim_{x \to x _0}f(x) = L $ . I s it n ec ess a ry tha t $f$  b e  de fined at th e po int $x_0$  itsel f ?
Well, what Ithinkofitis t h at  i t's  O K  to be  un d efi ned at t ha tpoint  bec a u s e  I g ues s th at wo n't cease the  li mito f t hat f uncti on t oexist  there  woul dit?

A:

"No",in a  particul arl ystr on g sen s e: The  ve ryreasonlimitsc ame  i n t o  m athematics was toex t r ac t numeri cal va l ue sf rom diff er enc e qu o t ients 
$$\ fr ac{f(x)- f(x_ { 0} )} {x - x_ {0 }}
$$(w hic h a re, o f  cou rse, a lgebraic allyi ndeterminate a t  $x_{0}$), in th e li m it a s $ x \to x_{0} $.
T h e fo rmal de fin i tionof $L  = \l i m(f, x_{0})$ ("Forev ery $\ varep silon > 0$, t here exist s a  $\delta  > 0 $  s u ch that if $0< |x- x_{0}| < \delta$,  then  $|f(x)- L| < \v a r epsilon$ ")exp lic itl y av oids evaluati o n  of$f $ at $x _{0 }$, pre cis ely  be cau se  $f$ migh t be und ef in ed  a t $ x_{0} $ .

A:

T hi s i snot  at a l l nece ssary . Fo rex a mpl e: $$
\ l im _ { x\to  0 }\fra c { x^ 2}x = 0, $ $ 
bu t $\lef t.\dfrac{ x^2 } {x}\ ri gh t\vert_ {x=0}$ is und ef ined.
If w edohave t h a t $f$ is  defined at $a$ and $\l i m\limit s_{ x\toa}f( x)=f(a)$,  th en $f$  is called  conti nuous  a t $ x = a$.
Q :
Re cu rsive call o n e rror
M y go al is a  function which ca n  ca ll itself aga ininde f i ni tel y  u p onen c oun t e ring an error.I am descr ib i ng  different app ro aches I  triedbased on theCommon Li sp HyperS pe c an d wou ld appreci ate if s omeone co u ld re v ea l the  se cretsof  wh y
the y acta s
ToString();
 _ _   _ __ __  _  _   _}
  __             __ }

A:

SPQuery.ListItemCollectionPosition_is_used_for paging in CAML queries,_but you can only use_saved values_of it to go to the page after_the_query that returned_the ListItemCollectionPosition

 Q:

Is it necessary that if a limit_exists at a point it should_be also defined_at_that_point?

Say there exists a_limit $\lim_{x \to x_0}f(x) = L$._Is it necessary that $f$ be_defined at the point $x_0$ itself?
Well, what_I think of it is that_it's OK to be undefined_at that_point because I guess that_won't cease the_limit of_that function to_exist there would it?

A:

"No", in a_particularly strong sense:_The very reason limits came into_mathematics_was to extract_numerical_values_from difference_quotients
$$
\frac{f(x) - f(x_{0})}{x_-_x_{0}}
$$
(which are,_of_course, algebraically indeterminate at $x_{0}$), in_the_limit as $x \to x_{0}$.
The formal definition_of $L = \lim(f,_x_{0})$_("For every $\varepsilon >_0$, there exists a $\delta_> 0$ such that if $0_< |x_- x_{0}|_< \delta$, then $|f(x) - L| < \varepsilon$") explicitly avoids evaluation_of $f$ at $x_{0}$, precisely because $f$ might_be undefined at $x_{0}$.

A:

This is_not at_all_necessary. For example:_$$
\lim_{x\to_0} \frac_{x^2}x =0, $$
but $\left.\dfrac{x^2}{x}\right\vert_{x=0}$ is undefined.
If we_do have_that $f$ is defined at $a$_and $\lim\limits_{x\to a}f(x)=f(a)$, then_$f$_is called continuous at $x=a$.

 Q:

Recursive_call on error

My goal is a_function which can call itself_again_indefinitely_upon
encountering an error.
I am describing_different approaches I tried based on_the Common Lisp_HyperSpec and would appreciate if someone could_reveal_the secrets of why
they act as