I have old 35mm lenses for my old Minolta camera. I'm going back to photography and getting an Olympus PEN E-PL1 (micro four thirds mount).  Can I use my old lenses on such a box or do they become completely useless? They were pretty expensive lenses, so why throw them away?
I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two.
Using the properties of real numbers, verify commutativity on complex numbers. I have just started self-studying Linear Algebra after a 3 year hiatus from mathematics (in an extended neuroscience foray), and I want to ensure that I am sufficiently verifying commutativity of complex numbers by using the properties of real numbers.  My attempts...  (1) Commutativity of Addition:   Verify that $w + z = z + w$ for all $w, z \in \mathbb{C}$.  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{16mm} = (a + c) + (bi + di) \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{19mm} = (c + a) + (di + bi) \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{13mm} = c + (a + di) + bi \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = c + (di + a) + bi \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{17mm} = (c + di) + (a + bi) \hspace{11mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{13mm} = z + w \hspace{34mm}\text{by definition of }\mathbb{C}$$  $$\blacksquare$$  This seems a bit verbose to me - is it acceptable to combine steps? For example, rather than:  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ can I instead write: $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{48mm} = a + (c + bi) + di \hspace{10mm}\text{by associativity and commutativity in }\mathbb{R}$$?  (2) Commutativity of Multiplication:  Verify that $wz = zw$ for all $w, z \in \mathbb{C}$.  $$\hspace{-14mm}wz = (a + bi)(c + di) \hspace{24mm}\text{by definition of }\mathbb{C}$$ $$\hspace{4mm} = a \cdot c + a \cdot di + bi \cdot c + bi \cdot di \hspace{10mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{9mm} = a \cdot c + bi \cdot c + a \cdot di + bi \cdot di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{35mm} = c \cdot a + c \cdot bi + di \cdot a + di \cdot bi \hspace{10mm}\text{by multiplicative commutativity in }\mathbb{R}$$ $$\hspace{1mm} = c(a + bi) + di(a + bi) \hspace{20mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{5mm} = (c + di)(a + bi)\hspace{34mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{4mm} = zw \hspace{55mm}\text{by distribution in }\mathbb{R}$$ $$\blacksquare$$  This also seems a bit wonky to me. Any and all suggestions on clearing up my verification, reasoning, etc. would be greatly appreciated! I'd like to highlight paragraphs such that the highlight color appears as one whole rectangle underlying the entire paragraph. I have looked around but nothing gives me the desired effect so far.  For example \fcolorbox{} from xcolor cannot highlight an entire paragraph; \hl{} from soul leaves out spacings between lines uncolored.  I am wondering how I can do this? Which IP address do I use to access my server? I'm running a Samba server on my MacBook and I've also set up port forwarding to said server from my router.  My public IP is 106.51.x.x (according to google and a few other services) and my Mac's local IP is 192.168.x.x, but when I head to my router's configuration page, it says my external IP is 10.242.x.x.  This is what I don't understand, when connected to my home WiFi, using the 10.242.x.x address works just fine. But if I try to access the same over 4G, the connection times out.  As for the public address, neither WiFi nor 4G works.  Is there some setting on my Mac (I'm running MacOS Sierra) that I must alter to make it visible to the public? Why doesn't the tilde (~) expand inside double quotes? According to  and my own understanding, the tilde expands to the home directory:  $ echo ~ /home/braiam   Now, whenever I want the shell expansion to work, i. e. using variable names such $FOO, and do not break due unexpected characters, such spaces, etc. one should use double quotes ":  $ FOO="some string with spaces" $ BAR="echo $FOO" $ echo $BAR echo some string with spaces   Why doesn't this expansion works with the tilde?  $ echo ~/some/path /home/braiam/some/path $ echo "~/some/path" ~/some/path Continuous function from $(0, 1]$ onto $(0, 1)$? Is there really no way to power a DSLR by USB? Is there any hint that the MoM or anywhere else got support in combating voldemort the first time around? Or is everything completely UK-centric?  I can't remember anyone in the second war being specifically sent from europe to help, even though we see international wizards in book 4. But I don't think all the events of the first war are covered in the books.  So are other bodies like the MoM involved in the first war, or was it isolated in the UK? Standard concise way to copy a file in Java? Convert from a specifc range to another one Take the following function:  DataTable go() {     return someTableAdapter.getSomeData(); }   When I set a breakpoint in this function, is there a possibility to inspect the returned value? go() is directly coupled to a datagrid in an .aspx page.  The only way to inspect the returned datatable is to use a temporary variable. However, that's a bit inconvenient. Isn't there another way? When are infinities okay? I'm a little confused about how to handle infinities in physics. On the one hand, I always here things like infinities are not physically tenable answers. GR can't answer anything about the origin of the universe because of singularities. Throw away the radial solution that gives an infinite potential when solving the Laplace equation in spherical coordinates. But then there are other times that the infinities are okay. For instance, it is usually okay to set the reference point for your potential at infinity. There are certain times in David Tong's quantum field theory lecture notes where he seems to almost to hand wave away infinities. So, philosophically, physically, and mathematically when are infinities okay, and when are they not okay? Play a Sound with Python There's already a question like this  so that my question could be considered duplicate, but I'll try to make my point clear that this is a different question.   Is there a way to derive  from the Lorentz' Force law or just from Maxwell's Equations?   The point is that we usually define, based on experiments, that the force felt by a moving charge on the presence of a magnetic field is $\mathbf {F} = q\mathbf{v}\times \mathbf{B}$, but in that case the magnetic field is usually left to be defined later.   Now can that force law be used in some way to obtain Biot-Savart law like we obtain the equation for the electric field directly from Coulomb's Force law?  I wanted to know that because as pointed out in the question I've mentioned, although Maxwell's Equations can be considered more fundamental, those equations are obtained after we know Coulomb's and Biot-Savart's laws, so if we start with Maxwell's Equations to obtain Biot-Savart's having use it to find Maxwell's Equations then I think we'll fall into a circular argument.   In that case, without recoursing to Maxwell's Equations the only way to obtain Biot-Savart's law is through observations or can it be derived somehow? Approximating $\arctan x$ for large $|x|$ I have been reading about depth-of-field and presume to have a sufficient understanding of what it means and how it is related to lens properties, lens aperture, focal length, sensor format size and probably even print dimensions in case the picture is being printed. I do have a question about how/if depth-of-field depends on the dimension of a pixel. Let me elaborate:  Given two sensors with differing pixel sizes: x and 4x, the latter sensor integrates more light per-pixel than the former, however, it might have a lower resolution if the sensor dimensions remain fixed. Theory suggests that the depth of field is determined by those circles-of-confusion which are very close to being an in-focus point, and this perhaps also means that these very small CoCs fall within the integration area of the same pixel. Now when a CoC becomes larger than a pixel (like also in the case of diffraction blur), there is some spreading of intensities among neighboring pixels and this would clearly lead to blur. However, if one was using the 4X sized pixel, even with a slightly larger CoC, the intensity would still integrate into the same pixel area, and would thus perhaps be in-focus? Is this the right assumption? And if so, is there any analysis of pixel-area dependence of depth-of-field? Moreover, depth-of-field is in some sense independent of the integration medium as it clearly occurs in analog film devices as well, so is there a trade-off or a difference in depth-of-field between film and digital cameras?  Please point me to the correct references for this question. Please correct me if there seems to be a fundamental issue with the assumptions made above. How to vertically align an image inside a div How can I change the margins for only part of the text? Sometimes the margins need to be changed for a particular page, paragraph, or other section of text.  For example, if I'm writing a letter and want the left margin to be almost at the right side of the page for the four lines of my address, or if I am combining prose with poetry and want the poems to be indented relative to the rest of the work.  What is the best way to change both left and right margins on the fly? How to avoid perceived circularity when defining a formal language? Suppose we want to define a first-order language to do set theory (so we can formalize mathematics). One such construction can be found . What makes me uneasy about this definition is that words such as "set", "countable", "function", and "number" are used in somewhat non-trivial manners. For instance, behind the word "countable" rests an immense amount of mathematical knowledge: one needs the notion of a bijection, which requires functions and sets. One also needs the set of natural numbers (or something with equal cardinality), in order to say that countable sets have a bijection with the set of natural numbers.  Also, in set theory one uses the relation of belonging "$\in$". But relation seems to require the notion an ordered pair, which requires sets, whose properties are described using belonging...  I found the following in Kevin Klement's,  (pages 2-3).  "You have to use logic to study logic. There’s no getting away from it. However, I’m not going to bother stating all the logical rules that are valid in the metalanguage, since I’d need to do that in the metametalanguage, and that would just get me started on an infinite regress. The rule of thumb is: if it’s OK in the object language, it’s OK in the metalanguage too."  So it seems that, if one proves a fact about the object language, then one can also use it in the metalanguage. In the case of set theory, one may not start out knowing what sets really are, but after one proves some fact about them (e.g., that there are uncountable sets) then one implicitly "adds" this fact also to the metalanguage.  This seems like cheating: one is using the object language to conduct proofs regarding the metalanguage, when it should strictly be the other way round.  To give an example of avoiding circularity, consider the definition of the integers. We can define a binary relation $R\subseteq(\mathbf{N}\times\mathbf{N})\times(\mathbf{N}\times\mathbf{N})$, where for any $a,b,c,d\in\mathbf{N}$, $((a,b),(c,d))\in R$ iff $a+d=b+c$, and then defining $\mathbf{Z}:= \{[(a,b)]:a,b\in\mathbf{N}\}$, where $[a,b]=\{x\in \mathbf{N}\times\mathbf{N}: xR(a,b)\}$, as in  question or  on Wikipedia. In this definition if set theory and natural numbers are assumed, then there is no circularity because one did not depend on the notion of "subtraction" in defining the integers.  So my question is:     Question Is the definition of first-order logic circular?   If not, please explain why.   If the definitions are circular, is there an alternative definition which avoids the circularity?   Some thoughts:   Perhaps there is the distinction between what sets are (anything that obeys the axioms) and how sets are expressed (using a formal language). In other words, the notion of a set may not be circular, but to talk of sets using a formal language requires the notion of a set in a metalanguage. In foundational mathematics there also seems to be the idea of first defining something, and then coming back with better machinery to analyse that thing. For instance, one can define the natural numbers using the Peano axioms, then later come back to say that all structures satisfying the axioms are isomorphic. (I don't know any algebra, but that seems right.) Maybe sets, functions, etc., are too basic? Is it possible to avoid these terms when defining a formal language? How to find the mime type of a file in python? Why is my crontab not working, and how can I troubleshoot it? This is a  about using cron &amp; crontab.   You have been directed here because the community is fairly sure that the answer to your question can be found below. If your question is not answered below then the answers will help you gather information that will help the community help you. This information should be edited into your original question.  The answer for 'Why is my crontab not working, and how can I troubleshoot it?' can be seen below.  This addresses the cron system with the crontab highlighted.