problems with mysql pdo query
Can PHP PDO Statements accept the table or column name as parameter?
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$ If $E$ is a connected space, then so is $\overline{E}$. I have to prove that if $E$ is a connected space, then so is $\overline{E}$ (the closure of $E$) a connected space. I tried to prove the contrapositive. So suppose that $\overline{E}$ is not connected in a metric space $X$. This implies there are $A\subset X$ and $B\subset X$ such that $A\cap B=\emptyset$, $A\cap \overline{E}\neq \emptyset$, $B\cap \overline{E}\neq \emptyset$ and $\overline{E}\subset A\cup B$. I will try to prove that this $A$ and $B$ will also work for $E$. Suppose that $A\cap E=\emptyset$ and $B\cap E=\emptyset$, this implies that $A\cup B$ is a subset of the limit points of $E$, because $A\cap \overline{E}\neq \emptyset$ and $B\cap \overline{E}\neq \emptyset$. This contradicts the fact that $\overline{E}\subset A\cup B$, so we have to conclude that $A\cap E\neq \emptyset\neq B\cap E$. Since $E\subset\overline{E}\subset A\cup B$, we have that $E$ is also not connected.  My question is whether my proof is correct, because I have a little bit doubt. If it's not correct, what is the best I can do? Thanks in advance!   Edit1: The definition we use for a connected space $E$ in a metric space $X$ is that if $E$ is connected, then there are no open $A,B\subset X$ such that $A\cap B=\emptyset$, $A\cap E\neq \emptyset\neq B\cap E$ and $E\subset A\cup B$.  Edit2: $A$ and $B$ must be open. Why "hide" Luke from his father somewhere Anakin knows? In Episode II Anakin goes to the Lars homestead and meets his extended family. How would sending Luke there be "hidden" to Vader in any way? At least Leia had a random planet and family. Why disable Fast Boot on Windows 8 when having dual booting? Given a dictionary, how can I find out if a given key in that dictionary has already been set to a non-None value?  I.e., I want to do this:  my_dict = {}  if (my_dict[key] != None):   my_dict[key] = 1 else:   my_dict[key] += 1   I.e., I want to increment the value if there's already one there, or set it to 1 otherwise. QGIS color polygon according to points I have two layers. Layer 1 contains points (x,y) and layer 2 contains one polygon. All points in layer 1 are positioned within the polygon of layer 2. The points in layer 1 contain an attribute with information on the topography/elevation at the specific point. Can I color the polygon in layer 2 based on attributes from the points in layer 1 in order to create an elevation map? Install 0bda:f179 Realtek Semiconductor Corp. (rtl8188fu), or Netgear rtl8812au USB WiFi adapters 19 DEC 2019 - I really, really wanted to use the Cinnamon desktop to set up a new system my 83-year-old Dad could navigate. I struggled to get any USB WiFi device working with Debian using Cinnamon, gave up and installed Ubuntu, but still struggled (I think) because I had immediately changed to the Cinnamon desktop before attempting to get the WiFi device set up.  It just kept prompting for the password, no matter what fixes I tried. Not sure if Cinnamon was the problem, or if I just hadn't found the right solution online. When I search for similar questions that I am going to ask, I usually can't find anything through the search box on Stack Overflow. But when I enter my question on the &quot;Ask Question&quot; page, the questions suggested through the &quot;Questions with similar titles&quot; box are usually relevant. Do you experience the same thing? How to hide password input from terminal in ruby script Activate physics by keyframe I'd like to have a group of debris fall from a ceiling onto the floor, but not have them drop all at the same time. Is there a way to set a keyframe that dictates when the object enters the simulation? For example, object 1 starts falling on frame 0, object 2 on frame 5, object 3 on frame 24, etc. Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$ Delete the entire table rendered from different pages using Javascript I'm completing a problem set, one problem for which I literally have no idea what to do on. The graders would prefer to have a physical copy of the problem so I thought it best to include the ¯\_(ツ)_/¯ emoji as my answer, instead of something like "Dunno" or "No idea."  Option #1 is to include an image.  Beyond that I actually don't understand how this emoji works. The middle character is Japanese kana "tsu" and proves problematic - TeX wants it in math mode then renders "?" when it is. Possible Duplicate:          I tried to color only a cell of my table but I don't know how do it. I found the method to color an entire row.How could I color only a cell of my table of a precise color? How to copy only file attributes (metadata) without actual content of the file? I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside? One of us is wrong, aren't we? I have just learned from what I consider a reliable source, that the following sentence is correct:     One of us is wrong, aren't we?   I would never in my life have written this, but I am assured that   As I realize comments don't live forever I will quote the relevant parts:     oerkelens : So you  would really write One of us is wrong, aren't we? I guess by analogy you would not bat an eyelid at One of these balls is blue, aren't they?   Matt Эллен : yes, "Then one of us is wrong, aren't we?" is exactly how it would be written. Same for the balls.   Could someone please enlighten me how it is possible that the number in a question tag supposedly has to be in discordance with the subject of the main clause?  I admit that I am not the youngest any more, and my school days are long gone, but back in the days, I was taught that  1. a verb and its subject concord in number 2. a question tag concords with the subject of the main clause  I was given examples like:     It is warm today, isn't it?   We will be on time, won't we?   Mary is pretty, isn't she?   John isn't the brightest, is he?   Some people may notice that the subject of the main clause seems to determine every time the subject of the question tag. When the main clause subject is singular, so are verb and subject in the question tag.  I was under the impression that a) this made sense and b) this would be a general rule.  I fully realize that grammar does not have to make sense, so a) is immaterial. As for b), today I learned I was wrong :)  So when (and possibly why?) do we form question tags that are different in number from their main clause?   To exemplify, also the other example sentence that I used and was corrected on:     One of these balls is blue, isn't it? (so this is wrong)   One of these balls is blue, aren't they? (and this is correct)   As an afterthought, does this strange grammatical number mix-up only appear in question-tags, or should I always refer to singular subjects in the plural if certain conditions are met? And what are those conditions?  Which versions are correct?     One of the cars is broken, aren't they? They (the car(s?) that is(are?) broken) should be fixed.   One of the cars is broken, aren't they? It (the car that is broken) should be fixed.   One of us must be wrong, mustn't we? We (the one(s?) that is (are?) wrong) should make amends.   One of us must be wrong, mustn't we? He (the one that is wrong) should make amends.   (In the last one, they could of course be used as the singular they, but that would avoid the issue...) What voltage is a 3-LED light from a LED-TV? I have some "NDV rev1.1 4248 back lights" from a television.   There is a print that sais "94V" on the strip, and on the wire supplying the strips it said "96V".   Every strip has 9x buttons which have 3 LED's in them. So i devided 94 by 9 and figured that every button should have 10.4V roughly, which makes sense, because a white LED is normally 3.5 volts.  I have a 12v Lithium battery which measured 11.1V so i tested one of the LED's with it and it lasted less than one second.   Are the LED's are rated for 10.4V roughly and not more? Use a concatenated (dynamic) string as JavaScript object key? It looks like Ubuntu 11.04 will come with  by default. I do like them, but I don't like the current mix of scrollbar types as many applications don't yet use those overlay scrollbars.  Is there a way to disable overlay scrollbars (without removing the overlay-scrollbar package)?