I'm planning to take a trip from Los Angeles to Houston, and found the ticket price is too high. However, I found a flight Los Angeles to Dallas/Fort Worth with a stop in Houston (LAX-IAH-DFW) that is more than $200 bucks less than the non-stop flight. Since I won't have any checked bags, can I just skip the IAH-DFW segment? What kind of problems could I run into if I do so (like being placed on the blacklist, shutting down my frequent traveler program, being charged for price difference, fine, etc.)? It's United I'm planning to take.
Say I want to book a flight from Fort Lauderdale to Chicago.  Say the airline also flies to St. Louis from Fort Launderdale but has a connecting flight through Chicago.  If I book that flights from FLL->ORD->STL and just get off in Chicago, what possible problems can I run into, assuming I didn't check any bags and only have carry on?  This scenario exist for Southwest, but I wanted this be more of a general question that would apply to all airlines.
I have two $2\times 2$ matrices, $A$ and $B$, with the same determinant. I want to know if they are similar or not.  I solved this by using a matrix called $S$: $$\left(\begin{array}{cc} a&amp; b\\ c&amp; d \end{array}\right)$$ and its inverse in terms of $a$, $b$, $c$, and $d$, then showing that there was no solution to $A = SBS^{-1}$. That worked fine, but what will I do if I have $3\times 3$ or $9\times 9$ matrices? I can't possibly make system that complex and solve it.  How can I know if any two matrices represent the "same" linear transformation with different bases?  That is, how can I find $S$ that change of basis matrix?  I tried making $A$ and $B$ into linear transformations... but without the bases for the linear transformations I had no way of comparing them.  (I have read that similar matrices will have the same eigenvalues... and the same "trace" --but my class has not studied these yet. Also, it may be the case that some matrices with the same trace and eigenvalues are not similar so this will not solve my problem.)  I have one idea. Maybe if I look at the reduced col. and row echelon forms that will tell me something about the basis for the linear transformation? I'm not really certain how this would work though? Please help. G is the product of its Sylow subgroups I want to prove the following:     If every Sylow subgroup of $G$ is a normal subgroup, then $G$ is isomorphic to the product of its Sylow subgroups.   So far, I have gotten to realize that for every prime factor $p_i$ of $|G|$, there is exactly one Sylow subgroup and that these form a partition of $G$. However, I am having trouble finding the isomorphism between $G$ and the product which I will call $G_1 \times \ldots \times G_r$. My idea was just to use the mapping $(g_1, \ldots, g_r) \mapsto g_1\ldots g_r$, which is a bijection, but I don't see whether it is a homomorphism. In general, not all elements of $G_i$ commute with elements of $G_j$, so one cannot simply change the order of the elements in the product. For as long as I can remember I have avoided using switch statement fall-through. Actually, I can't remember it ever entering my consciousness as a possible way to do things as it was drilled into my head early on that it was nothing more than a bug in the switch statement. However, today I ran across some code that uses it by design, which got me immediately wondering what everyone in the community thinks about switch statement fall-through. Is it something that a programming language should explicitly not allow (like C# does, though it supplies a workaround) or is it a feature of any language that is powerful enough to leave in the programmer's hands? Edit: I wasn't specific enough to what I meant by fall-through. I use this type a lot:     switch(m_loadAnimSubCt){         case 0:         case 1:             // Do something             break;         case 2:         case 3:         case 4:             // Do something             break;    }  However, I'm concerned about something like this.    switch(m_loadAnimSubCt){         case 0:         case 1:             // Do something, but fall through to the other cases             // after doing it.          case 2:         case 3:         case 4:             // Do something else.             break;    }  This way whenever the case is 0, 1 it will do everything in the switch statement. I've seen this by design and I just don't know if I agree that switch statements should be used this way. I think the first code example is very useful and safe. The second seems kind of dangerous. How would one go about proving that the rationals are not the countable intersection of open sets? I ride regularly in the city with my a few valuables with me. My purse, phone, keys, company ID card etc. I hate having a bag on me while ride so I am looking for a solution to have these few items in a bike bag, but also have them safe if I stop somewhere to run into  a shop or a cafe for 15 minutes.   My original idea was to look for a small saddle or top tube bag that is lockable and also safely locked to the frame, and I can simply leave it there. As it turns out there is no such thing! Or I just did not find it?  My second idea was to search for a similar bag, but which is easily detachable and I can take it with myself as a waist bag for example. Same story, I couldn't find anything like this on the market.  Do you know any bag that could work for me? Or do you have an alternate suggestion for my conundrum?   Thank you very much if you take the time to answer! Ride safe! János Single-word synonym for "immensely valuable"? I am looking for some (may be rarely know to nonnative English speakers) synonyms for  "immensely valuable" or "extremely valuable". I know if $\ i\ $  of the following form $\ 3x^2 + (6y-3)x - y\ $ or $\ 3x^2 + (6y-3)x + y - 1, \ \ x,y \in \mathbb{Z}^{+},i \in \mathbb Z_{\ge 0}$,  then $\ 12i + 5\ $ must be composite number, because:  $12(3x^2 + (6y-3)x + y - 1) + 5 = 36x^2 + (72y - 36)x + (12y - 7) = (6x + 12y - 7)(6x  + 1)$  How come if $\ i\ $ not of the following form $\ 3x^2 + (6y-3)x - y\ $ and $\ 3x^2 + (6y-3)x + y - 1\ $,  then $12i + 5$ must be prime? $\ x,y \in \mathbb{Z}^{+},i \in \mathbb Z_{\ge 0}$.  For example: $\ 5 = \ 3*1^2 + (6*1-3)*1 - 1\ $ ,when $\ x = y = 1\ $, as proved before,$\ 5*12+5\ $ must be composite number;  $\ 0, \ 1. \ 2.\ 3.\ 4\ $ can't of the following form $\ 3x^2 + (6y-3)x - y\ $ and $\ 3x^2 + (6y-3)x + y - 1\ $,  $\ 12*0 + 5 = 5\ $, $\ 5 $ is prime,$\ 12*1 + 5 = 17\ $, $\ 17 $ is prime, and so on, Change name on the main Stack Exchange profile Integrity constraints in a relational database - should we overlook them? I’m in a permanent discussion with the developers of the company where I work because they say it is better to get rid of relationship enforcement (via FOREIGN KEY constraint definitions) in a relational database in order to speed up large queries and to gain better performance. The platform under consideration is MySQL 5.x, and no FOREIGN KEY has been set up, even some PRIMARY KEY constraints of the relevant tables are missing which, at least for me, is not reasonable. Maybe they’re right and I’m wrong, but I don’t have enough arguments to discuss about this situation. This has been the preferred approach for three years now. I’m new in this company (only one month) but, as the product “works”, there is hesitation to enhance the database; nevertheles, the first thing I noticed is one page taking 1 minute to load (yes, 60 seconds!). One of the claims behind the current state of affairs is that a “denormalized” database is faster than a normalized one, but I don’t believe that’s true. Most of the relevant queries include JOIN operations, which makes them run very, very, very slow with large amounts of data (the database contains millions of rows). Commonly, the handling of “CRUD” operations is implemented at the application program code level; for example, in order to DELETE some data FROM, let’s say, TableA:  it is necessary to first check on the fly if there is some relationship between the rows of TableA and TableB, in case that said relationship is “detected”, then the app program code won’t allow to DELETE the pertinent row(s), but if for some reason the app program code fails, then the DELETE operation will “succeed”, no matter if there is any relationship regarding the involved rows and tables.  Question Could you help me to elaborate a good, accurate and solid answer to enrich the debate?  Note: Maybe something like this has been asked (and answered) before, but I couldn’t find anything by means of Google. Dollar Sign corrupts question In  my question () contains a "$" in a quoted section of the question.  Originally I had a second "$" in a second quoted  section of the same question.    However when I did this the second $ seemed to trigger a style that made the text italic and lost spacing between words.  I took out the second "$" and instead emphasized it with the word "dollars" which solved the immediate problem.  However, in the listing of the question, (not the question itself) the same thing happens after the first "$".  The summary shows the text without spaces between words and in italic.  Seems like a bug.  Below is a verbatim copy/paste of the original issue (two dollar signs):    I was able to find a small ESC for about $12 off of ebay.  If you were designing a robot, would you see that and think?       $12 bucks for an ESC that connects to simple pulse-wave interface -   sign me up!   Or would you think:     $12 just to control a motor? I could throw together an H-bridge for   $0.50 and be done with it.   My robot in particular actually has two motors and therefor $24 to control the two of them.  But the interface is really easy (plus has the added advantage of being R/C vs computer controlled with a simple change of connectors.  Which way would you go? Why is there a difference between ping "localhost" and ping "local IP address"? Using cmd and ping on Windows gave me the following results:   Pinging "localhost":       Pinging "192.168.0.10" (local IP address):     Aren't both situations exactly the same?   I mean, I'm pinging the same interface, the same machine and the same address. Why do I get such different results?  EDIT: Here is my ipconfig /all screen: How to remove Gmail from iPad mail? Why does it take so long to review a flag suggested by a user? Why does it take so long to review a flag suggested by a user?  When I flag a question or comment, some get a response quickly whereas some of them get a response after few or more hours.  Is there any flag review condition which cause so much time to be taken for different flags?  Or are there different moderators for different flag posted? Restricted logins with automatic full permission in databases My scenario: I have some groups with full - and inappropriate - access to all Sql Server instances. I want to change that.  My Plan: Give full and automatic access to all databases (it is customer databases and this groups must be allowed to change any property if necessary).  Restrict permissions on Instance Level, because this groups should not be allowed to do any unexpected change on instance properties.  I don't want to create a user in databases, because our external customer could drop the user ( they have db_owner permission )  Someone have any idea? Tks Fit a table into one page If $f(x)$ is differentiable at x, I need to prove that $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$ exist and is finite.  so if $f(x)$ is differentiable at a $x$, the difference quotient exist for this point, and also $f(x)$ must be continuous at x as well  so that mean that:  $\lim_{h\to0^+}\frac{f(x+h)-f(x)}{h} =  \lim_{h\to0^-}\frac{f(x+h)-f(x)}{h}$  and that: $\lim_{x\to x_0^+}=\lim_{x\to x_0^-}=f(x_0)$  I know I should probably use arithmetic limit laws to prove this but I can't see how what I figured out could help me. any help with that?  Thanks! What is the formal definition of polynomial ring of several variables? Let's consider a polynomial ring of single variable. One can define them informally by saying $P(X)=\sum_{i=1}^n a_n X^n$ while $X$ is an indeterminate variable. However, since mathematics is based on first-order logic, one can only talk about something that actually exists (as a set). So as its name says, indeterminate variable is not a sentence in $ZFC$. Nevertheless, we can formally define a polynomial ring $R[X]$ as a subset of $R^\omega$ whose support is finite. ($R$ is a commutative ring with unity) Just like a single variable, I want to know what would be the formal definition of a polynomial ring of several variables. What would be a formal definition? === I have figured out a candidate. That is,  Candidate for a &quot;Definition of a polynomial ring $R[X_1,...,X_n]$&quot;. ($R$ is a commutative ring with unity) Let $R[X_1,...,X_n]$ be the set of all functions $f:\omega^n \rightarrow R$ whose support is finite. Define $(f+g)(a,b,c)=f(a,b,c)+g(a,b,c)$ and $(f•g)(a'',b'',c'')=\sum_{a+a'=a''} f(a,b,c)•g(a',b',c')$ (Note that in this way, $+,•$ are well defined.) Then, it can be checked that $(R[X_1,...,X_n],+,•)$ is a ring.  Is this a formal definition of a polynomial ring? When to use \LetLtxMacro? Frequently I see users redefine macros using (for example)  \let\oldmacro\macro% Store \macro in \oldmacro \renewcommand{\macro}{%   % ...redefined \macro   \oldmacro% }   and other times they use  \usepackage{letltxmacro}% http://ctan.org/pkg/letltxmacro \LetLtxMacro{\oldmacro}{\macro}% Store \macro in \oldmacro \renewcommand{\macro}{%    % ...redefined \macro   \oldmacro% }   Why would one use \LetLtxMacro when \let works just as well? Or, more specifically, when would one use \LetLtxMacro and/or why? Solving ODE with negative expansion power series I am solving a series of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  $g_{ii}$ are given, from metric, but that's not important. I need to assume that the solution (since I'm looking for components of $\xi^\mu$, which is a vector with components $\xi^t,\xi^r,\xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$, and this is to be seen as expansion around $1/r$ (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where   $\xi^\mu_{n,i}$   is the derivative with the respect to i-th component.   What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my $\mathcal{O}(r)$ terms cancel each other out? Or?  I'm kinda stuck :\ How to delete specific lines from a txt file I have a Bash script that writes data into a log file, then from that I take out stuff I want using the sed command. That gives me a file data.txt. What I want to know is how I go about deleting specific line inside that data.txt file.  For example:  123 456 789   I want to remove the 2nd line, containing 456 so that I only have  123  789   I tried with sed '2d' data.txt but it doesn't work.  I use this command to create data.txt from log.log:  sed -nE '1s/.{1}(.{2}).*/\1/p;' log.log &gt;&gt; data.txt