A  says     teachers and test graders want to see the words trying to instead of tryna.   I understand this sentence clearly.  I just wondering whether "rather than" could be substituted for "instead of".  I  and  gives some clear rules (I modified it a little bit)     (rule#1) "Instead of" is used when you were given a plan and you want to change it.       (rule#2) "Rather than" connotes a situation where you are asked about something and you like both options and you need to choose your favorite.   I suppose most VOA articles use the correct words though, the use of words does not seem to be a plan. That is more like the rule#2.  Which rule is supposed to be used in this context? Are "instead of" and "rather than" interchangeable in the case?
I have a sentence:     Please show me the right way so that I can do that rather than take blind action.     Is this sentence grammatically correct?   Can I use instead of to replace rather than? If replaced, the meaning of this sentence is changed?   What is the difference between rather than and instead of? Can you show me some examples to distinguish them?
headed or heading, started or starting? Consider:  Two units are headed your way. Two units are heading your way. Don't get me started! Don't get me starting!  Is there any difference in meaning? And I don't see why passive voice is used here. I would think they have similar meaning here. Help me to clarify! Calculating RSA private exponent when given public exponent and the modulus factors using extended euclid How to change hair color along length of strand? At some point (not right away), I'll be wanting to make a character model which has multicolor hair.  Namely, it will be one color closer to the roots, and another color closer to the tips.  Is there any way to do this in blender?  I would be using Cycles for this. Can an ideal in a commutative integral domain be its own square? If $I$ is a non-zero proper ideal of a commutative integral domain, is it possible for $I$ to be its own square? How do I remove directories that begin with a dot after my server was infected? My server had been infected and the attacker spread a bunch of .5randomletters folders around my file system, with malicious code inside of them. I want to search for all the folders that begin with a dot, review them and then remove them.  How can I do that? I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course, it's always good to give as much intuition about the material.  Some things I'd be happy if it includes (but again, it mostly just needs to be a clear book even if it doesn't contain these) are:   As much justifications for the postulates if possible, I'm very interested in reading more about how Liouville's theorem connects to the postulates. Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas. Block specific URL on web browsers I want to block certain URLs on browsers. I don't want to block whole site. For example, I want to block , but not whole  domain. Is there any way I can do it? Formal Proof that area of a rectangle is $ab$ I tried to prove that the area of a rectangle is $ab$ given side lengths $a$ and $b$.  The best I can do is the assume the area of a $1\times1$ square is $1$. Then not the number of $1\times1$ squares that fit in an $a\times b$ rectangle is $ab$. Therefore area is $a\cdot b$. This does not seem rigorous however. Claim: if $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.   Please, see if I made some mistake in the proof below. I mention some theorems in the proof:   The condition to $f(x)$ be continuous at $x=x_0$ is $\lim\limits_{x\to x_0} f(x)=f(x_0)$.  (1) If $f(x)$ is differentiable at $x-x_0$, then $f'(x)=\lim\limits_{x\to x_0} \dfrac{f(x)-f(x_0)}{x-x_0}$ exists and the function is defined at $x=x_0$.   (2) Therefore, by the Limit Linearity Theorem, $\lim\limits_{x\to x_0} f(x)$ exists and we'll show it is equals $f(x_0)$.   (3) We'll do this by the Precise Limit Definion: given $ \epsilon&gt;0, \exists\delta|0&lt;|x-x_0|&lt;\delta$, then $0&lt;|f(x)-f(x_0)|&lt;\epsilon$. As this limit exists by (2), we can make $f(x)$ as close to  $f(x_0)$ as one wishes, therefore $\lim\limits_{x\to x_0} f(x)=f(x_0)$, what satisfies the condition for $f(x)$ be differentiable at  $x=x_0$. The end. Does $\sum_{k=1}^{\infty}\ln(\frac{k}{k+1})$ converge/diverges?? Does this series converge or diverge? $$\sum_{k=1}^{\infty}\ln(\frac{k}{k+1})$$   my thought is that, I can break it down to $$\sum_{k=1}^{\infty}\ln(k) - \sum_{k=1}^{\infty}\ln(k+1)$$ then maybe using comparison test or something? But I don't know exactly how to prove whether this series converges or diverges.  Any help would be appreciated! How to determine equality for two JavaScript objects? A strict equality operator will tell you if two object types are equal. However, is there a way to tell if two objects are equal, much like the hash code value in Java?  Stack Overflow question  is similar to this question, but requires a more academic answer. The scenario above demonstrates why it would be necessary to have one, and I'm wondering if there is any equivalent solution. Want to fill line with repeating string Similar to the \dotfill command, but with your own text, rather than dots.  If the string was: kitty!  The entire line would look like the following: kitty!kitty!kitty!kitty!kitty!kitty!kitty!kitty!kitty!  Is there any way to do this? ISP blocking port 25 I have a problem called "The Prison Problem" that I need to explain to my 9-year-old cousin. I would think that he has just started learning about divisors and perfect squares, and as such, I have a proposed solution. Any input from you guys would be welcome, as to what is the best way to go about this.  Problem:  There was a jail with 100 cells in it, all in a long row. The warden was feeling very jolly one night and told his assistant that he wanted to give all the prisoners a wonderful surprise. While they were sleeping, he wanted the assistant to unlock all the cells. This should be done, he told the assistant, by putting the key in each lock, turning it once. The assistant did this, then came back to report that the job was done. Meanwhile, however, the warden has second thoughts. "Maybe I shouldn't let all the prisoners free," he said. "Go back and leave the first cell open, but lock the second one (by putting the key in and turning it once). Then leave the third open, but lock the fourth, and continue in this way for the entire row." The assistant wasn't very surprised at this request as the warden often changed his mind. After finishing this task, the assistant returned, and again the warden had other thoughts. "Here's what I really want you to do," he said. "Go back down the row. Leave the first two cells as they are, and put your key in the third cell and turn it once. Then leave the fourth and fifth cells and turn the key in the sixth. Continue down the row this way." The assistant again did as instructed. Fortunately, the prisoners were still asleep. As a matter of fact, the assistant was getting pretty sleepy, but there was no chance for rest yet. The warden changed his mind again, and the assistant had to go back again and turn the lock in the fourth cell and in every fourth cell down the row. This continued all through the night, next turning the lock in every fifth cell, and then in every sixth, and on and on, until on the last trip, the assistant just had to turn the key in the hundredth cell. When the prisoners finally woke up, which ones could walk out of their cells?  Proposed solution:  Ten cells are left open after this process. Every cell that is a perfect square will remain open (1, 4, 9, 16, 25, 36, 49, 64, 81, and 100). If a number is not a perfect square, then it has an even number of divisors, therefore it will be "toggled" an even number of times and end up where it started (closed). Perfect squares have an odd number of divisors, so they will end up the opposite of where they started (open). How do I find out a name of class that created an instance of an object in Python if the function I am doing this from is the base class of which the class of the instance has been derived?  Was thinking maybe  might have helped me out here, but it doesn't seem to give me what I want. And short of parsing the __class__ member, I'm not sure how to get at this information. How to send data to a serial port and see any answer? On Linux, I want to send a command string (i.e. some data) to a serial port (containing control characters), and listen to the response (which also usually might contain control characters).   How can I do this as simplest as possible on Linux? An example is appreciated! I am going to change my machine: from a laptop with Ubuntu to another laptop where I am going to install Ubuntu...  I am quite happy with the current system, what I am afraid of is having to rebuild everything from 0.  So what do people often do to clone an Ubuntu system? That may include the data, packages, shortcut settings, etc... Finding information on German soldiers from World War I and World War II? Where can I find information on German soldiers from World War I and World War II?   I am curious to find out about my ancestors' role in the wars, i.e. what rank they had, where they where fighting, with whom and anything else. Limit Ordinal Question how to prove this result.     $\alpha$ is limit ordinal if and only if $\beta&lt;\alpha$ implies $\beta+1&lt;\alpha$ for any $\beta$.   I am getting confused because of the definition of limit ordinal. it says     $\alpha=\sup\{\beta: \beta&lt;\alpha\}=\bigcup\alpha$    for sup I am ok but for $\alpha=\bigcup\alpha$ how ?? Efficiently replace all accented characters in a string?