When I open MS Paint (Win 8), the default border thickness is set to the thickness depicted in the picture.    Is there a way to change the default rectangle border thickness?
After closing paint the last used settings went back to default. I want them to be saved. Like the selected Brush-Tool, Color, Line-strength, etc.  Either after every usage or I define one I use most. Maybe through the registry or by start parameters?
incoming mail just sits in the drop folder This is a  about DNS glue records.   What exactly (but briefly) is a DNS glue record?  Why are they needed and how do they work? Short, Politically Correct word for Native Americans No more than four syllables, more PC than Indians.  EDIT: I arbitrarily chose four syllables because any more seemed like a mouthful. I like to be PC and not have to stumble over 6+ syllables. Redirect parent window from an iframe action "Everything is a file" in the UNIX World.  Above sentence is famous. When I run echo "hello programmer" &gt;&gt; /dev/tty1 , I can watch the given string on TeleType 1  , ....  What and where is file per each socket? Suppose my friend connects to my PC, and its IP is h.h.h.h , how can I access the respective file? Is it possible? Derivative of function with 2 variables I've leart in Calculus 1 that the derivetive of $f(x)$ is:  $$\lim_{h\to0} \frac{f(x+h) - f(x)}{h}$$.  suppose $f(x,y)$ is a function with 2 variables,  does $$f'(x,y) = \lim_{h\to0} \frac{f(x+h, y+h) - f(x,y)}{h}$$ ?  If not , what is the derivetive of function with 2 variables? I want to know a proof of an alternative form of Fermat-Euler's theorem   $$a^{\phi (n) +1} \equiv a \pmod n$$   when $a$ and $n$ are not relatively prime.   I searched some number theory books and a cryptography book and internet, but there were only proofs of the original theorem  $a^{\phi (n)} \equiv 1 \pmod n$ or in case n=pq which is used for RSA. So I would be very thankful if someone show me a proof or book I should read. I want to know if there is another way to solve the equation:  $$(x+1)^y-x^z=1$$  for positive integers $x,y,z$ greater than $1$ without using the Catalan identity. Does exist? By now I only know that $x\mid y$. "Single ampersand used with wrong catcode" error using tikz matrix in beamer This is a generic inquiry on the common practice/standard for determining the acceptable values of RMS when georeferencing topographic maps.  Is there an absolute value?  Some literature suggests that it should be "less than or equal to 1/2 of the side of a cell which make up the total resolution of the image." MathJax isn't currently working on the Android app, which makes it totally useless for the 'technical' sites like  or .  For example, in the Android app:    Same post in a (mobile) browser:     Please add this functionality! What are these  error below ?  Package natbib Warning: Citation `Krishna2014' on page 16 undefined on input li ne 502.  [16 &lt;./figure/aks smr.png&gt;] [17] [18] ! Undefined control sequence. l.560 \Bibliography                    {figure/bib} Finite groups with exactly one maximal subgroup I was recently reading a proof in which the following property is used (and left as an exercise that I could not prove so far). Here is exactly how it is stated.     Let $G$ be a finite group. Suppose it has exactly one maximal subgroup. Then $G$ is cyclic.   Now, does this mean exactly one conjugacy class of maximal subgroups? If it really means exactly one maximal subgroup, then what can we say about a finite group that possesses exactly one class of (at least two) maximal subgroups that are all conjugate to each other? There are many (duplicate) questions about the acceptance, popularity and history of singular they (and their, them and themself) around here, it even got a tag of its own. If I didn’t miss anything, however, the proper verb form hasn’t been questioned yet.  As we all know, English third person singular pronouns (it, she, he and one, +body), names (Alice, Bob, …) and nouns (student, teacher, …) demand the +(e)s suffix be added to the finite verb form in simple present, where some auxiliary verbs have a “special” form (is &lt; *bes / *ares and has &lt; *haves). All other subjects don’t, including plural third person pronoun they.  When the plural you replaced thou (with thee, thy / thine), the other marked verb form that had remained in English – i.e. suffix +(e)st or +t – vanished, too. The first and second persons only ever appear as pronouns (I, we; you), not names or nouns, so there was no strong inclination to keep the verbal inflection.  The second person precedent would suggest that singular they be used with uninflected verb forms which is how it’s usually encountered in the wild. Assuming that they someday replaces he and she (and maybe it) it would lead to disagreement with the words the pronoun stands in for:        Alice         goes to her   place  by herself.   Bob           goes to his   place  by himself.   Alice and Bob go   to their place  by themselves. – (common)   Alice and Bob go   to their places by themselves. – (separate)                  She  goes to her   place  by herself.   He   goes to his   place  by himself.   They go   to their place  by themselves.   They go   to their places by themselves.                  They ?goes to their place  by themself.   ditto   They  go   to their place  by themselves.   They  go   to their places by themselves.                  They ?go to their place  by ?themselves.   ditto   They  go to their place  by  themselves.   They  go to their places by  themselves.      So why doesn’t singular they afford s on present-tense verbs like all other third person singular subjects do?   I learned about singular they only long after I had been taught English as a second language in school. That’s why it’s still a conscious decision to use it and hence I could easily adapt to use s forms with it, but would that sound and look funny / strange / wrong to native speakers? What does "calculus" mean? "calculus" and "formal system"  From      a calculus is a formal system that consists of          a set of syntactic expressions (well-formed formulæ or wffs),    a distinguished subset of these expressions (axioms), plus    a set of formal rules that define a specific binary relation on the space of expressions.      From      Formal systems in mathematics consist of the following elements:         A finite set of symbols (i.e. the alphabet), that can be used for constructing formulas (i.e. finite strings of symbols).   A grammar, which tells how well-formed formulas (abbreviated wff) are constructed out of the symbols in the alphabet. It is   usually   required that there be a decision procedure for deciding whether a   formula is well formed or not.   A set of axioms or axiom schemata: each axiom must be a wff.   A set of inference rules.      what is the difference between a formal system, and a calculus, then? I think they are the same? "calculus" and "logic system"  "Calculus" appears in "propositional calculus" and "first-order predicate calculus", which are also called "propositional logic" and "first-order logic" respectively. So I thought "calculus" and "logic" mean the same, and "a logic" is, according to ,      A logical system or, for short, logic, is a formal system together with a form of semantics, usually in the form of model-theoretic   interpretation, which assigns truth values to sentences of the   formal language, that is, formulae that contain no free variables.    But then I saw "calculus" also appears in "lambda calculus", which is also a formal system. I think a lambda calculus isn't a logic system, right? What does "calculus" mean in "lambda calculus"? Furthermore  "calculus" can also mean computational real analysis for first-year college students.   Thanks. What is a token? Please forgive such a basic question, but I did some Google searching and looked around on this site,  and while there are many threads and online resources that involve tokens, I can't seem to find a direct explanation of what a token is, specifically in the context of TeX, LaTeX, etc. Perhaps there is a good explanation of tokens in the TeXbook, but I don't have a copy of it.   gives me some idea:     A token is a string of characters, categorized according to the rules as a symbol (e.g., IDENTIFIER, NUMBER, COMMA).   but this is a bit too general for me to understand. Taking a guess based on the Wikipedia definition and , is it correct to say that a token is "a thing that has a catcode"? (which, even if true, does not seem entirely satisfactory as an answer: what characterizes the things that are given catcodes?)  Some illustrative examples, and non-examples, of tokens in the realm of TeX, LaTeX, etc. would be much appreciated. All Stack Exchange data dumps A doubt from Milnor's "Topology from a Differentiable Viewpoint". This is a doubt from Milnor's "Topology from a Differentiable Viewpoint".     For a smooth $f:M\to N$, with $M$ compact, and a regular value $y\in N$, we define $n(f^{-1}(y))$ to be the number of points in $f^{-1}(y)$. It is easy to see that $n(f^{-1}(y))$ is finite. It can also be seen that $n(f^{-1}(y))$ is locally constant; i.e. there is a neighbourhood of $y$ such that for every point $y'$ in that neighbourhood, $n(f^{-1}(y'))=n(f^{-1}(y))$.   The proof for the statement in bold is the following:     Let $x_1,x_2,\dots,x_n$ be the points of $f^{-1}(y)$, and choose disjoint neighbourhoods $U_1,U_2,\dots,U_n$ of these points, which are mapped diffeomorphically into neighbourhoods $V_1,V_2,\dots,V_n$ of $y$. The required neighbourhood is $(V_1\cap V_2\cap\dots V_n)-f(M-U_1-U_2-\dots U_n)$.   I don't understand how $(V_1\cap V_2\cap\dots V_n)-f(M-U_1-U_2-\dots U_n)$ is open. I know that $(V_1\cap V_2\cap\dots V_n)$ is open. However, how can one prove that $f(M-U_1-U_2-\dots U_n)$ is closed? I can see this working if $f$ is surjective, but not otherwise. Exercise $7$, page 51 from Hungerford's book Algebra.     Show that $N=\{(1),(12)(34), (13)(24),(14)(23)\}$ is a normal subgroup   of $S_{4}$ contained in $A_{4}$ such that $S_{4}/N\cong S_{3}$ and   $A_{4}/N\cong \mathbb{Z}_{3}$.   I solved the question after many calculations. I would like to know if is possible to define an epimorphism $\varphi$ from $S_{4}$ to $S_{3}$ such that $N=\ker(\varphi)$.  Thanks for your kindly help. Finding an example of a discrete-time strict local martingale.