Broad and wide are near synonyms but only near, since "a broad smile" is a more common collocation than "a wide smile", and you can say "eyes wide open" but not "eyes broad open".  Breadth and width seem to be closer synonyms since both are defined in Collins Dictionary Online as:     the linear extent or measurement of something from side to side   Why are the adjectives/adverbs broad and wide not as interchangeable as the nouns breadth and width seem to be?
Could you help me to point out the differences in the following sentences. for me both sentences imply same meaning.      The Restaurant , offers a broad range of locally caught fresh seafood,   prime steak and meat dishes      The Restaurant , offers a wide range of locally caught fresh seafood,   prime steak and meat dishes
Vito and Luca question Why is this simple Excel calculation not netting Zero? How to do a generalized linear model with multiple dependent variables in R? I have six dependent variables (count data) and several independent variables, I see that in a MMR the script goes like this:  my.model &lt;- lm(cbind(DV1,DV2,DV3,DV4,DV5,DV6) ~ IV1 + IV2 + ... + IVn)   But, since my data are counts, I want to use a generalized linear model and I tried this:  my.model &lt;- glm(cbind(DV1,DV2,DV3,DV4,DV5,DV6) ~ IV1 + IV2 + ... + IVn, family="poisson")   And appears this error message:  Error in glm.fit(x = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  :    (subscript) logical subscript too long`   Can anyone explain me this error message or a way to solve my problem? What are the left and right ideals of matrix ring? How about the two sided ideals? Different behaviour for list.__iadd__ and list.__add__ I cannot boot to the desktop because I filled the file system. How do I reclaim some space? My memory is completely full when I tried following the data recovery and copied the wrong file using command line tool Test Disk. As it was taking so long to copy, I turned it off and I realized I copied the wrong file. Now my laptop memory is now full and lead me to more problems.  I have had similar problems to :       Now my screen keeps blinking:   Can anybody help? Many thanks. Wish you all the best. Where are the default settings saved for the Command Prompt defaults?  Are they stored in the registry somewhere, or in a file?  I would love to make a .reg file to set my default preferences when logging into a machine for the first time.  I'm talking about the default application settings: QuickEdit mode, buffer size, text color, etc. Brownian motion - Hölder continuity Let $B$ stand for a Brownian motion on a finite interval $[0,1]$. If I am not wrong, I think that there exists a positive constant $c$, such that almost surely, for $h$ small enough , for all $0&lt; t &lt; 1- h$  \begin{align} |B(t+h)-B(t)| &lt; c\sqrt{h\log(1/h)} \end{align} or something like this. As a result   \begin{align} \bigg|\frac{B(t+h)-B(t)}{h}\bigg| &lt; K(h)  \end{align}  Am I correct ? How to set the default value of an exposed filter rather than -Any-? I have a view with exposed filters in Drupal 7 and I need to set the default value of a filter to current year. I also need to unset/remove the - Any - option from the select list. Why am I getting black photos when I use the Manual feature on my DSLR? I was taking photos a few days ago, and I had it set to Manual. After about four photos, the rest started coming out black. I could see through my eyepiece clearly, and it took the photo normally, but when I reviewed it they were all black. What color are Nissa, Worldwaker's lands? When I check for updates, I get a "Failed To Download Repository Information" error.   This is what comes up under details:   W: Failed to fetch gzip:/var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_natty_main_source_Sources  Hash Sum mismatch,  E: Some index files failed to download. They have been ignored, or old ones used instead. Difference between "right of=" and "right=of" in PGF/TikZ In the PGF/TikZ manual, sometimes I see the option right of=somenode instead of right=of somenode. They look very similar, but the effects are different.  The distance between nodes positioned with the latter option is boundary-to-boundary, as stated in the manual. However, with the first option, it seems that the distance is shorter. I couldn't find any explanation of the first option in the manual.  My question is: what is the difference between the two options? Is there any explanation in the manual that I missed? How much money do you need to have on hand when entering USA? My friend, a Chilean citizen, is entering the US via waiver program to spend 3 weeks in USA in a couple of weeks. She already got her ESTA approval, the plane ticket, all hotels are already booked (but paid by me, not her).  How much money would she need to bring with her when entering US? Do they still check this? She would of course have credit cards with her. If humans were able to catch all sun energy reaching the earth for their use, will the climate change? I guess that energy will be used up and, at the end, will contribute to heat the earth, so I see no big differences...  please explain your point of view. Why is there a difference between urls submitted to a sitemap and urls in the google index? What's the weight of the earth? What's the weight of the earth?  That is, what's the weight of the earth in the gravitational field of the sun? I imagine it's either   $0$, because there's no net fall toward the sun, so the downward component of acceleration is $0$ and $F=ma=0$, or $Gm_1m_2/r^2\approx7\cdot10^{-11}\cdot6\cdot10^{24}\cdot2\cdot10^{30}/(1.5\cdot10^{11})^2\approx4\cdot10^{22}$ Newtons,   but which, and why? Why don't we consider centrifugal force on a mass placed on earth? Why do we use this definition of "algebraic integer"? A number is an &quot;algebraic integer&quot; if it is the root to a monic polynomial with integer coefficients. Artin says (Algebra, p. 411):  The concept of algebraic integer was one of the most important discoveries of number theory. It is not easy to explain quickly why it is the right definition to use, but roughly speaking, we can think of the leading coefficient of the primitive irreducible polynomials $f(x)$ as a &quot;denominator.&quot; If $\alpha$ is the root of an integer polynomial $f(x)=dx^n+a_{n-1}x^{n-1}...$ then $d\alpha$ is an algebraic integer, because it is a root of the monic integer polynomial $x^n + a_{n-1}x^{n-1} + ... + d^{n-1}a_0$. Thus we can &quot;clear the denominator&quot; in any algebraic number by multiplying it with a suitable integer to get an algebraic integer.  When I first learned of algebraic integers, I looked online and saw some hints that maybe they were used to prove the Abel-Ruffini theorem. So I put off questioning their usage for a while; I now think I understand one proof of this theorem (the one at the end of Artin's Algebra) and it has nothing to do with algebraic integers (that I can tell). So basically: why is it important if a number is an algebraic integer? I think I understand what he's saying about the relationship between roots of integer polynomials and algebraic integers, but I fail to see why this is &quot;one of the most important discoveries of number theory.&quot; I have a problem , i can't open synaptic >:(  root@dopeboy:~# synaptic No protocol specified ** (synaptic:6940): WARNING **: Could not open X display No protocol specified (synaptic:6940): Gtk-WARNING **: cannot open display: :1   I have try to Re-install it but is not working, any idea how to fix?! VPS Ubuntu 14.04 LTS.