Is it possible to analytically solve the expression $x^{x^x}=3$? And how to solve this problem numerically? Simply testing some results, I found that $\sqrt{2.6}&lt;x&lt;\sqrt{2.7}$. What matches the result provided by  in the comments. But in addition to a numerical solution, like the technique posted by , is it possible to find a &quot;closed&quot; formula for the solution of this problem?
We can solve the equation $x^x=c$ using the Lambert $W$ function, but how do we solve $x^{x^x}=c$ ,
SQLite parameter substitution problem Using SQLite3 with Python 2.5, I'm trying to iterate through a list and pull the weight of an item from the database based on the item's name.  I tried using the "?" parameter substitution suggested to prevent SQL injections but it doesn't work. For example, when I use:  for item in self.inventory_names:     self.cursor.execute("SELECT weight FROM Equipment WHERE name = ?", item)     self.cursor.close()   I get the error:     sqlite3.ProgrammingError: Incorrect number of bindings supplied. The current statement uses 1, and there are 8 supplied.   I believe this is somehow caused by the initial creation of the database; the module I made that actually creates the DB does have 8 bindings.  cursor.execute("""CREATE TABLE Equipment      (id INTEGER PRIMARY KEY,      name TEXT,     price INTEGER,      weight REAL,      info TEXT,      ammo_cap INTEGER,      availability_west TEXT,     availability_east TEXT)""")   However, when I use the less-secure "%s" substitution for each item name, it works just fine. Like so:  for item in self.inventory_names:     self.cursor.execute("SELECT weight FROM Equipment WHERE name = '%s'" % item)     self.cursor.close()   I can't figure out why it thinks I have 8 bindins when I'm only calling one. How can I fix it? Ubuntu with spyware? Richard Stallman states that Ubuntu "has installed surveillance code". See:   Is this true?   I agree with him that "Any excuse Canonical offers is inadequate....". putExtra treeMap returns HashMap cannot be cast to TreeMap android I have got a new installation of windows recently. Now when I do unpin items from taskbar that were there (IE, Edge, Explorer), they do come back after restart. A pinned chrome does not disappear though e.g.  Anything to fix this issue?  P.S. Just created a new user, and he has the same problem  P.P.S. Sign out is enough to get it back, no full restart needed "In the case of medical diagnostics, there is a cost associated with each medical procedure that provides additional information (blood test, x-ray, etc.)."   Should that end with "etc.).", "etc)." or "etc.)"? Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$ What do you call something that is not first in a sequence? Is there a word to describe something that is not the first element in a sequence, but can be in any other position? A synonym of "not first", in fact.     This element is __ in this sequence. I want OSM administrative boundaries from . I can get the geodata in different formats there, but the attribute data always is a separate JSON file. I want them both in just one file, or to be able to merge the information.   I haven't found a solution to merge the GeoJSON.   What's the workflow to get the two files joined and saved as a shapefile, for example? How to draw a fish? I would like to draw an image like the following.     This is what I've done so far (I used tikz, but any other package is welcome):  \documentclass{article} \usepackage{tikz}  \begin{document}     \begin{tikzpicture}         \draw[fill=blue] (.5,0) rectangle (4,2);         \draw[fill=red] (1,1) to[bend left=50] (3,1) to[bend left=50] (1,1);         \draw[fill=red] (3,1) -- (3.5,1.5) -- (3.3,1) -- (3.5,.5) -- cycle;         \draw[fill=white] (1.6,1.1) circle (.15cm);          \draw[fill=blue] (1.55,1.1) circle (.05cm);              \end{tikzpicture} \end{document}     Edit: April 2nd, Time for explanation  In Italy (but I also think in other countries), a practical joke done on April 1st is called "pesce d'Aprile" (= April's fish, that is an ) and is often related to fishes.  The usual one is to stick a drawing of a fish on someone's back without he/she realizes it.  Some years ago a colleague of mine stuck some "pesci d'Aprile" with written below "sono disponibile" (= I'm easy) on the rear of all the cars in our company car parking. Some other colleagues didn't realize it, and they had gone around with that drawing for days.  Another funny example happened in Milan . Someone put on the windshield of a lot of cars a false fine for illegal parking. On the fine sheet was written "per il pagamento rivolgersi agli uffici comunali di via Gadio, 2" (= for payment, please contact the municipal offices in via Gadio, 2), the address of the Civic Aquarium.  Hence, this question was simply a way to put    P.S. = Since I earned a lot of reputation points with this trick question, I decided to give them back to the Community awarding a bounty to the two answers posted on April, 1st.  Moreover, I accepted Robert's one since he guessed without spoiling, and I thank the other two answerers.  To the downvoters: you're probably technically right, but:   there's already too much sadness in the world, let's laugh now and then! humor is part of the LaTeX philosophy, Prof. Knuth himself docet if only serious questions are accepted, why did they create a fun tag? I have to prove that a function $f:]0,1] \rightarrow \Bbb R$ : $$ f(x) = \begin{cases} \frac1q,  &amp; \text{if $x \in \Bbb Q$  with $ x=\frac{p}q$ for $p,q \in \Bbb N$ coprime} \\ 0, &amp; \text{if $x \notin \Bbb Q $} \end{cases} $$  is discontinuous in every point $x \in \ ]0,1] \cap\Bbb Q$.  And then to consider $x \in \ ]0,1] \backslash \Bbb Q$ and prove that it is continuous.  For now I learned different ways to prove continuity (epsilon-delta, sequences), but I'm never sure what would be better to use in each different case.  I wanted to prove the discontinuity by using sequences: $$\forall x_n \quad x_n\rightarrow a \quad \Rightarrow \quad f(x_n) \rightarrow f(a)$$  I tried creating a sequence $ x_n=\frac1n + a$, we know it converges to $a$ but $f(x_n)\ $ doesn't  converges to $\ f(a)$ because there would still be some points not in our set (irrational numbers that creates gaps).  But I don't think it works, so I'm asking you if you could help me solving the two questions. Case insensitive 'Contains(string)' Is there a way to make the following return true?  string title = "ASTRINGTOTEST"; title.Contains("string");   There doesn't seem to be an overload that allows me to set the case sensitivity.. Currently I UPPERCASE them both, but that's just silly (by which I am referring to the  issues that come with up- and down casing).  UPDATE This question is ancient and since then I have realized I asked for a simple answer for a really vast and difficult topic if you care to investigate it fully. For most cases, in mono-lingual, English code bases  answer will suffice. I'm suspecting because most people coming here fall in this category this is the most popular answer.  answer however brings up the inherent problem that we can't compare text case insensitive until we know both texts are the same culture and we know  what that culture is. This is maybe a less popular answer, but I think it is more correct and that's why I marked it as such. What is a word that means "someone who pretends to be your friend but is actually your enemy?" What do you call someone who pretends to be your friend but is actually your enemy?  A friend suggested spy for me, but that does not nearly describe the word I need for an English project. The character is very good at manipulating how people see him. He's a good liar. And pretends to be your friend but actually is your enemy. I'd like to loop though each feature in a layer and calculate its ellipsoidal area using QgsDistanceArea() in PyQGIS 3.  Everything works fine on unprojected layers, but I get strange results when input layer is in projected CRS.  So far I have written this:  from qgis.core import *  def calculate_area(in_lyr_name, ellipsoid, units):     input_layer = QgsProject.instance().mapLayersByName(input_lyr_name)[0]      area = QgsDistanceArea()     area.setEllipsoid(ellipsoid)      features = input_layer.getFeatures()     feature_area = 0     error_features_counter = 0      for i, feat in enumerate(features):         geom = feat.geometry()         polygon_area = 0         try:             if geom.isMultipart():                 polygons = geom.asMultiPolygon()                 for polygon in polygons:                     polygon_area += area.measurePolygon(polygon[0])             else:                 polygon = geom.asPolygon()                 polygon_area = area.measurePolygon(polygon[0])              feature_area += polygon_area          except AttributeError:  # catches NoneType geometries (broken etc.)             error_features_counter += 1             pass      # calculated area is in sq. metres (see the "else" case)     if units == 'km²':         final_area = feature_area / 1e6     elif units == 'Ha':         final_area = feature_area / 10000     else:         final_area = feature_area     return final area, error_features_counter   How do I get a constant result that does not depend on the presence of projection? Can spells be cast through a Wall of Force? Proper way to exit iPhone application? I am not very well versed on set theory or syntax, but I thought I knew the basics.  However, in a book about databases I am reading now, the author uses $2^x$ to signify "a set of $x$."  For example, $2^{\text{dogs}}$ is a set of $\text {dogs}$, etc.    The author never really explained this or why he does it, I just picked up the meaning from context.    I am not sure why the exponent operator is used, nor am I sure what the number $2$ has to do with it.  The sets being represented are NOT powers of $2$ (in size)... they come in all sizes.  Is this a valid notation?  I have not seen it anywhere before... bash prompt messed up on arrow up I have made some modification to my prompt with use of colors via tput.  It looks like now when I try to do an arrow up lookup after few moves up, the prompt is being cut into half, what I mean by this is:  From this:  PROD mysuer@server1.domain.com:~$ vim .bashrc   To this:  PROD mysuer@servegit rebase origin/add_pool   ctrl + c brings everything back to normal.  I have found some posts indicating that this may be due to the issue with missing escapes for [ however I don't see an issue here:  My code:  #red for prod, green for lab  COLOUR_RESET=$(tput sgr0) COLOUR_GREEN=$(tput setaf 2) COLOUR_BLUE=$(tput setaf 6) COLOUR_YELLOW=$(tput setaf 3) COLOUR_RED=$(tput setaf 1) BOLD=$(tput bold)  if [[ $HOSTNAME =~ .*\.domain.com$ ]]; then   COLOUR=$COLOUR_RED   PROMPT_TEXT="PROD" fi  if [[ $HOSTNAME =~ .*\.lab$ ]]; then   COLOUR=$COLOUR_BLUE   PROMPT_TEXT="LAB" fi   MYPROMPT="$COLOUR$BOLD$PROMPT_TEXT$COLOUR_RESET \[\u@$COLOUR$BOLD$(hostname -f)$COLOUR_RESET:\w\]\$ "  PS1=$MYPROMPT   UPDATE: @KamilMaciorowski has pointed out a similar question although it was not relating to a tput colors. Microsoft recommends using Rowversion over timestamp, but I can not find "rowversion" data type inside my sql server 2008 R2 Microsoft  mentioned that we should use the rowversion data type over Timestamps. Now inside my SQL Server 2008 R2, I want to create a column with the Rowversion data type. But in my SQL Server 2008 R2 Management Studio, I cannot find such a data type:  Also when I tried altering existing column named timestamp which is of type timestamp using this statement: ALTER TABLE [SkillManagement].[dbo].[Customer] ALTER COLUMN timestamp rowversion   I get this error: Msg 4927, Level 16, State 1, Line 1 Cannot alter column 'timestamp' to be data type timestamp  Can anyone advise? EDIT Assume that $f$ be continuous on $\mathbb{R}$, $f'(x)$ exists for all $x\neq 0$, and $\lim_{x\rightarrow 0} f'(x)=1$. We need to show $f'(0)$ exist and is equal to $1$.  $f'(0)=\lim_{x\rightarrow 0}\frac{f(x)-f(0)}{x}$, $\lim_{x\rightarrow 0}f'(x)=1\Rightarrow\lim_{x\rightarrow 0}\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=1$...am I going in the right direction? Please help. Difference between least squares and minimum norm solution Consider a linear system of equations $Ax = b$.   If the system is overdetermined, the least squares (approximate) solution minimizes $||b - Ax||^2$. Some source sources also mention $||b - Ax||$. If the system is underdetermined one can calculate the minimum norm solution. But it does also minimize  $||b - Ax||$, or am I wrong?   But if least squares is also a minimum norm, what is the difference, or the rationale of the different naming?