Is there single word that describes that I learned and became proficient in using a skill but is not as strong as mastered.  I want to say, "I (blank)ed a new technique." I learned it, but I have also become quite proficient in using it. Although I am proficient, I wouldn't say I have mastered the technique.
I'm looking for the noun form of "person with intermediate skill". For example, in the context of a particular activity, "person with no skill" might be designated a novice, and "person with much skill" might be designated an expert. However I know of no such word in between these two extremes.   My only thought is amateur, which has a distinct meaning from describing level of skill, although skill level can often be inferred. I'm looking for a better solution.  EDIT: due to the attention this question has received, I'll try to offer some clarification in order to reduce repeat questions.   "Journeyman" would certainly not work. I am a software developer by profession. However the word I'm looking for should hopefully be profession-agnostic. I am trying to designate the skill level of the person that some learning material might be appropriate for. The word that I'm looking for follows the preposition "for".   For Beginners  For [word for intermediate-skilled person] For Experts  Sorry, but even after all the great answers, I'm still learning towards "amateur" even though it is technically incorrect. Also, the word should not be so esoteric that only people with English degrees know what it means. Keep the ideas coming!
Is 'clamp' a formally recognized mathematical function? I was surprised to find the clamp function absent from  and . Is this mainly a concept particular to computer programming? Is it known by another name in mathematics? I'll be editing the Wikipedia shortly to include a reference to this function but I want to make sure I'm not omitting some synonymous terms I'm currently unaware of.  $$   \operatorname{clamp}(x) = \max( a , \min( x , b ) ) \in [a,b] $$ How do I install an individual package on a Linux system? Getting opencv error in c++ I found an argument online that the two fields are not isomorphic but I can't make sense of the argument. You find it .  These are the things I'm confused about when it comes to the argument.     It says that the field $\mathbb Q[x]/(x^2+1)$ contains a root of the polynomial $x^2+1$. I suppose this is the congruence class $[x]$? But this is not the same as the zero element of the field $\mathbb Q[x]/(x^2+1)$, right?   It says that every isomorfism takes $0$ to $0$. I interpret this as the zero-element in $\mathbb Q[x]/(x^2+1)$ (which I interpret to be $[0]$) is taken to the zero-element in $\mathbb Q[x]/(x^2+2)$ denoted $[0]_2$. But in the argument it says that this means that if $\mathbb Q[x]/(x^2+1)$ has a root of the polynomial, then also $\mathbb Q[x]/(x^2+2)$ must have a root of this same polynomial. Why is that?     Greatful for any help! Encrypting a key with the same key, for instance using AES I am new to crypto and trying to understand if it would be insecure to use a cipher such as AES to encrypt a key with the same key. If it is insecure, then why would it be insecure?  Basically, something like this:  encrypt(key, key)   What happens when both key and message are the same (128 bits)?  The obvious question would be why would I want to do that. If I have a secure channel to send the key, why encrypt it? My question is more for understanding. Using contracted forms ("don't", "let's") in a formal text How compelled should I feel to use non-contracted forms (do not rather than don't and so on) when writing in a rather formal text, say an academic paper? In one case I am afraid to seem too stilted, in the other, too casual. Are there good guidelines?  And are there differences in this regard between British and American English?  (In this  there was not much more than "Contractions are more frequent in informal than formal contexts".) In school, I have always seen sets. I was watching a video the other day about functors, and they started talking about a set being a collection, but not vice-versa. I also heard people talking about classes. What is their relation? Some background would be nice.   It has to do with something called Russell's paradox, but I don't know what that is.   I think that the difference between a family and a set is that the former is a function and the latter is a set. Is this right? Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$ I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof? Show reference label when it is undefined When a reference is undefined, LaTeX shows simply [??] which doesn't give much information. I would like it to show the label instead. This is useful when more collaborators work on the same preprint and the references are yet to be done.  I'm using neither biblatex nor natbib. I do use bibtex but it is irrelevant for this question.  MWE:  \documentclass{article}  \begin{document}  This: \cite{undef} should look like: [{\bfseries ?? undef}]  \end{document} Can Muggles publicly establish the existence of a magical community? VMware won't work after Ubuntu Upgrade I upgraded to Ubuntu 15.10 and now if I want to open VMware Player it doesn't do anything. I also uninstalled and installed it again, still nothing.  What can I do? I am trying to prove that the affine hull of a set $X \subseteq \mathbb{R}^d$ is equal to the affine hull of the clojure of that set: $$ \text{aff}(X) = \text{aff}(\text{cl}(X)). $$  Proving $\text{aff}(X) \subseteq \text{aff}(\text{cl}(X))$ is easy, but containment in the other direction is harder.  I am assuming there is a sequence $\{ x_k \}_{k=1}^\infty \subseteq X$ such that $\lim_{k\to \infty} x_k = x^*$. The point $x^*$ is obviously contained in $\text{aff}(\text{cl}(X))$. But I am not sure how to show it is also in $\text{aff}(X)$, specifically because I am not sure how to show that $x^*$ lies on a line connecting two points in $X$.  Any suggestions on how to surmount this hurdle are welcome. If $\mathbb f$ is analytic and bounded on the unit disc with zeros $a_n$ then $\sum_{n=1}^\infty \left(1-\lvert a_n\rvert\right) \lt \infty$ I'm going over old exam problems and I got stuck on this one. Suppose that $\mathbb{f}\colon \mathbb{D} \to \mathbb{C}$ is analytic and bounded. Let $\{a_n\}_{n=1}^\infty$ be the non-zero zeros of $\mathbb{f}$ in $\mathbb{D}$ counted according to multiplicity. Show that  $$ \sum_{n=1}^\infty \left( 1 - \left|a_n \right|\right)\lt\infty $$  I can understand that $\left|a_n \right|$ goes to $1$ since zeros are isolated, but it doesn't help showing the series is convergent. Any help will be appreciated! How can I tell how long (more or less) it will take me to complete a game? I'm going down my huge backlog of unplayed Steam games and I'm thinking the best way to tackle the list is to go through the shortest games first and then concentrate on the 20+ hour ones. I'm wondering if there's a website or something else that has an estimated amount of gameplay time for games.   Is there anything like that? Does Time Machine backup programs like Photoshop and iWork? ^x^y unix trick for all instances in last command? One of my favorite Unix tricks is ^x^y, which will take the last command and replace the first instance of "x" with "y". However, I'm wondering if a similar trick works to replace all instances of "x" with "y" in the last command? A property of every real polynomial. Question: For every polynomial $P(x)$ of degree at n we have $$\sum_{i=0}^{n+1}(-1)^i\binom{n+1}{i}P(i)=0$$  Well I was inducting on degree of the polynomial, for $n=0$ its true and I got a bit confused in the inductive step, actually I cant figure the inductive step.   Is this property (if true) a famous one?  Thank you for your help. Should I install graphics card drivers from Windows Update? Ordered N-Tuples as Cartesian Products of Indexed Families In Introduction to Topology, Mendelson defines the Cartesian Product of an Indexed Family as follows:     DEFINITION  Let $\{X_\alpha\}_{\alpha \in I}$ be an indexed family of sets. The product  of the sets $\{X_\alpha\}_{\alpha \in I}$,    written  $\prod_{x\in I}X_\alpha$ consists of all functions $x$ with domain the indexing set $I$ having the property that for each $\alpha \in I$, $x(\alpha)\in X_\alpha$.    Halmos, in Naive Set Theory, makes the following observation about this sort of product:     Ordered triples, ordered quadruples, etc., may be defined as families whose index sets are unordered triples, quadruples, etc.   However, it is not immediately apparent to me why this is true. It makes sense if we understand the prior assertions in Halmos that $\prod_{i \in I} X_i = X_i$ and that $\prod_{i \in I} X_i = X_a \times X_b$ when $I = \{a, b\}$, but these already pose difficulty for me.  Let $I = \{0, 1\}$, let $X_0 = \{A, B\}$, and let $X_1 = \{C, D\}$. Then by Mendelson's (and Halmos's) definitions, it would seem to me that . . .  $$\prod_{i \in I} X_ i = \{\{(0, A), (1, C)\}, \{(0, A), (1, D)\}, \{(0, B), (1, C)\}, \{(0, B), (1, D)\}\}$$  This would appear to me to be the set of all functions matching the definition given, but it is not equal to $X_0 \times X_1$. Moreover, extending this to a case where the index set $I$ is a triple, we would not end up with ordered triples, but with each subset of the product containing three ordered pairs.  When Halmos posits the equalities he does, the idea seems easy to grasp, but the peculiar wording of Mendelson's definition suggests something different to me. The  EU book The Rise and Fall of Darth Vader reveals that Vader personally gave the stormtroopers the order to kill Owen and Beru Lars, and that he knew who he was condemning to death before he gave the order:  “Lord Vader,” said one of the sandtroopers, adjusting a control on his helmet so that only Vader could hear his voice.  “The Jawas sold a protocol droid and an astromech to these moisture farmers, but both droids are gone.” Moisture farmers? Intrigued, Vader examined the holograms of the kneeling couple and said, “The farmers’ names?” “Owen and Beru Lars, sir,” the sandtrooper responded. “They say they don’t know where the droids are, but it looks like a landspeeder is missing from their garage.” Owen and Beru, Vader recalled... “Tell Mr. and Mrs. Lars that they seem to have trouble keeping protocol droids on their property.”1 Not certain if he had heard correctly, the sandtrooper said, “Sir?” “Then you may extend to them every courtesy that you showed the Jawas before you continue your search. Establish checkpoints to detain any droids entering Mos Espa or Mos Eisley spaceports. And one more thing.” “Yes, Sir?” “Do not stop transmitting until I break the connection.” “Understood,” said the sandtrooper. Vader watched the sandtroopers carry out his orders on their helpless victims. He found the sight of rising flames — even holograms of flames burning millions of light years away — to be most satisfying.  I had always assumed that the stormtroopers killed the Larses on their own initiative, or in accordance with a previously given order.  The version of events in this book is interesting, but it raises the question of why it took Vader so long to figure out who Luke was. In canon, who gave the order to kill Owen and Beru Lars?  If Vader was involved, did he recognize the couple before he gave the order?  1 A reference to the fact that Anakin took C-3PO from the Lars homestead the last time he was on Tatooine, without informing the Larses that he would do so.