Can't connect to Access database ("architecture mismatch" error)
The specified DSN contains an architecture mismatch Error
Unit ball in $C[0,1]$ not sequentially compact This question is taken from Saxe K -Beginning Functional Analysis.   Show that the closed unit ball in $C[0,1]$ is not compact by proving that it is not sequentially compact.   (It's assumed that we are using the uniform norm).  I've been working on this for ages but I could not come up with any sequence $\{f_n\}$ in the unit ball such that there exists $N\in \mathbb{N}$ such that for all $m,n\geq N$ we have that $d(f_n,f_m)&gt;c$. Should be a nice example of this, please help me! Given the key, the plain text and the cipher text can I calculate the IV used in CBC mode? If I have the plain text, the ciphertext and the key for an AES-128 CBC operation, can I determine the IV, even if I don't know the padding (assuming the padding follows one of the more common formats)?  I believe it should be possible since my understanding is that the IV is only used as an initial XOR of the plain text in encryption, and should, therefore, be able to be available like this:  AESDecrypt(key, ciphertext) =&gt; (PlainText XOR IV); IV = ((Plaintext XOR IV) XOR (Plaintext))   Is this correct? I'm trying to match SHA1's in generic text with a regular expression.  Ideally I want to avoid matching words.   It's safe to say that full SHA1's have a distinctive pattern (they're long and a consistent length) - so I can match these reliably - but what about abbreviated SHA1's?  Can I rely on the presence of numbers?  Looking at the SHA1's in my commit log - numbers always appear in the first 3 characters. But is this too short? How many characters of SHA1 do I need to consider before I can assume a number would have appeared?    This does not have to be 100% accurate - I just need to match an abbreviated SHA1 99% of the time. I've been reading the  and it mentions about virtual terminals which, if I understood it correctly, it is a Linux-specific feature (not in Unix) to allow multiple login consoles in a non X11 system. You create virtual terminals by pressing ALT-F2. I'm running Linux Mint and in my /dev folder though I see many tty devices and I don't know what they are for. Here is the grepped output:  crw-rw-rw-  1 root tty       5,   0 Jan  2 19:45 tty crw--w----  1 root tty       4,   0 Jan  2 19:10 tty0 crw-rw----  1 root tty       4,   1 Jan  2 19:10 tty1 crw--w----  1 root tty       4,  10 Jan  2 19:10 tty10 crw--w----  1 root tty       4,  11 Jan  2 19:10 tty11 crw--w----  1 root tty       4,  12 Jan  2 19:10 tty12 crw--w----  1 root tty       4,  13 Jan  2 19:10 tty13 crw--w----  1 root tty       4,  14 Jan  2 19:10 tty14 crw--w----  1 root tty       4,  15 Jan  2 19:10 tty15 crw--w----  1 root tty       4,  16 Jan  2 19:10 tty16 crw--w----  1 root tty       4,  17 Jan  2 19:10 tty17 crw--w----  1 root tty       4,  18 Jan  2 19:10 tty18 crw--w----  1 root tty       4,  19 Jan  2 19:10 tty19 crw-rw----  1 root tty       4,   2 Jan  2 19:10 tty2 crw--w----  1 root tty       4,  20 Jan  2 19:10 tty20 crw--w----  1 root tty       4,  21 Jan  2 19:10 tty21 crw--w----  1 root tty       4,  22 Jan  2 19:10 tty22 crw--w----  1 root tty       4,  23 Jan  2 19:10 tty23 crw--w----  1 root tty       4,  24 Jan  2 19:10 tty24 crw--w----  1 root tty       4,  25 Jan  2 19:10 tty25 crw--w----  1 root tty       4,  26 Jan  2 19:10 tty26 crw--w----  1 root tty       4,  27 Jan  2 19:10 tty27 crw--w----  1 root tty       4,  28 Jan  2 19:10 tty28 crw--w----  1 root tty       4,  29 Jan  2 19:10 tty29 crw-rw----  1 root tty       4,   3 Jan  2 19:10 tty3 crw--w----  1 root tty       4,  30 Jan  2 19:10 tty30 crw--w----  1 root tty       4,  31 Jan  2 19:10 tty31 crw--w----  1 root tty       4,  32 Jan  2 19:10 tty32 crw--w----  1 root tty       4,  33 Jan  2 19:10 tty33 crw--w----  1 root tty       4,  34 Jan  2 19:10 tty34 crw--w----  1 root tty       4,  35 Jan  2 19:10 tty35 crw--w----  1 root tty       4,  36 Jan  2 19:10 tty36 crw--w----  1 root tty       4,  37 Jan  2 19:10 tty37 crw--w----  1 root tty       4,  38 Jan  2 19:10 tty38 crw--w----  1 root tty       4,  39 Jan  2 19:10 tty39 crw-rw----  1 root tty       4,   4 Jan  2 19:10 tty4 crw--w----  1 root tty       4,  40 Jan  2 19:10 tty40 crw--w----  1 root tty       4,  41 Jan  2 19:10 tty41 crw--w----  1 root tty       4,  42 Jan  2 19:10 tty42 crw--w----  1 root tty       4,  43 Jan  2 19:10 tty43 crw--w----  1 root tty       4,  44 Jan  2 19:10 tty44 crw--w----  1 root tty       4,  45 Jan  2 19:10 tty45 crw--w----  1 root tty       4,  46 Jan  2 19:10 tty46 crw--w----  1 root tty       4,  47 Jan  2 19:10 tty47 crw--w----  1 root tty       4,  48 Jan  2 19:10 tty48 crw--w----  1 root tty       4,  49 Jan  2 19:10 tty49 crw-rw----  1 root tty       4,   5 Jan  2 19:10 tty5 crw--w----  1 root tty       4,  50 Jan  2 19:10 tty50 crw--w----  1 root tty       4,  51 Jan  2 19:10 tty51 crw--w----  1 root tty       4,  52 Jan  2 19:10 tty52 crw--w----  1 root tty       4,  53 Jan  2 19:10 tty53 crw--w----  1 root tty       4,  54 Jan  2 19:10 tty54 crw--w----  1 root tty       4,  55 Jan  2 19:10 tty55 crw--w----  1 root tty       4,  56 Jan  2 19:10 tty56 crw--w----  1 root tty       4,  57 Jan  2 19:10 tty57 crw--w----  1 root tty       4,  58 Jan  2 19:10 tty58 crw--w----  1 root tty       4,  59 Jan  2 19:10 tty59 crw-rw----  1 root tty       4,   6 Jan  2 19:10 tty6 crw--w----  1 root tty       4,  60 Jan  2 19:10 tty60 crw--w----  1 root tty       4,  61 Jan  2 19:10 tty61 crw--w----  1 root tty       4,  62 Jan  2 19:10 tty62 crw--w----  1 root tty       4,  63 Jan  2 19:10 tty63 crw--w----  1 root tty       4,   7 Jan  2 19:10 tty7 crw--w----  1 root tty       4,   8 Jan  2 19:10 tty8 crw--w----  1 root tty       4,   9 Jan  2 19:10 tty9 How are unmarketable market orders (other side of the order book is empty) matched with incoming orders? Trying to install Steam ERROR: You are missing the following 32-bit libraries, and Steam may not run: not I've already installed Steam, but when I click on the program I get this message  ERROR- You are missing the following 32-bit libraries, and Steam may not run: not   I don't know what to install or even do. How can I take a screenshot with Selenium WebDriver? Prove inequality $\sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3$ How do I free up more space in /boot? My /boot partition is nearly full and I get a warning every time I reboot my system. I already deleted old kernel packages (linux-headers...), actually I did that to install a newer kernel version that came with the automatic updates.  After installing that new version, the partition is nearly full again. So what else can I delete? Are there some other files associated to the old kernel images?  Here is a list of files that are on my /boot partition:  :~$ ls /boot/ abi-2.6.31-21-generic         lost+found abi-2.6.32-25-generic         memtest86+.bin abi-2.6.38-10-generic         memtest86+_multiboot.bin abi-2.6.38-11-generic         System.map-2.6.31-21-generic abi-2.6.38-12-generic         System.map-2.6.32-25-generic abi-2.6.38-8-generic          System.map-2.6.38-10-generic abi-3.0.0-12-generic          System.map-2.6.38-11-generic abi-3.0.0-13-generic          System.map-2.6.38-12-generic abi-3.0.0-14-generic          System.map-2.6.38-8-generic boot                          System.map-3.0.0-12-generic config-2.6.31-21-generic      System.map-3.0.0-13-generic config-2.6.32-25-generic      System.map-3.0.0-14-generic config-2.6.38-10-generic      vmcoreinfo-2.6.31-21-generic config-2.6.38-11-generic      vmcoreinfo-2.6.32-25-generic config-2.6.38-12-generic      vmcoreinfo-2.6.38-10-generic config-2.6.38-8-generic       vmcoreinfo-2.6.38-11-generic config-3.0.0-12-generic       vmcoreinfo-2.6.38-12-generic config-3.0.0-13-generic       vmcoreinfo-2.6.38-8-generic config-3.0.0-14-generic       vmcoreinfo-3.0.0-12-generic extlinux                      vmcoreinfo-3.0.0-13-generic grub                          vmcoreinfo-3.0.0-14-generic initrd.img-2.6.31-21-generic  vmlinuz-2.6.31-21-generic initrd.img-2.6.32-25-generic  vmlinuz-2.6.32-25-generic initrd.img-2.6.38-10-generic  vmlinuz-2.6.38-10-generic initrd.img-2.6.38-11-generic  vmlinuz-2.6.38-11-generic initrd.img-2.6.38-12-generic  vmlinuz-2.6.38-12-generic initrd.img-2.6.38-8-generic   vmlinuz-2.6.38-8-generic initrd.img-3.0.0-12-generic   vmlinuz-3.0.0-12-generic initrd.img-3.0.0-13-generic   vmlinuz-3.0.0-13-generic initrd.img-3.0.0-14-generic   vmlinuz-3.0.0-14-generic   Currently, I'm using the 3.0.0-14-generic kernel. Change this behavior to allow for spelling corrections and the like: "Edits must be at least 6 characters" Now, it is easy to workaround this: add 10 characters, plus your one-character change, then remove these 10 characters in the next edit for the same post.  But this can hardly be what the designers intended. Instead, my suggestion is to change it to something like on Wikipedia, where you can mark an edit as "minor". Something like this:     Edits must be at least 6 characters, or select the checkbox "Minor, spelling or punctuational correction."   Edits like that will, of course, not count toward the edit-limit (before it becomes Community Wiki).  The suggestion often seen on Meta Stack Overflow is "just edit more in that post". But sometimes the post is just right, and there aren't any other spelling mistakes to correct. Why force a user to change more than necessary, or use an ugly hack? General formula for evaluating integrals of the form $\displaystyle\int_0^\infty x^ae^{-bx}dx$ Find a general formula for evaluating integrals of the form $\displaystyle\int_0^\infty x^a e^{-bx}dx.$   I've been pondering about this question for some time. Obviously integration by parts is way too inefficient. I know there's recursion involved and maybe there's a way to find a general formula through intuition. How to know current name of the database in Django? Properties of p-adic valuations Let $n$ be a integer not equal to zero, $p$ a prime and $$|n|_p = p^{-\operatorname{ord}_p(n)}; |0|_p=0$$  Proposition: $|xy|_p=|x|_p|y|_p$  We want to show: $\operatorname{ord}_p(ab)=\operatorname{ord}_{p}(a)+\operatorname{ord}_p(b)$ So if we suppose there is a largest integral $v$ such that $p^{v}|(ab)$, then we can split up v such that $p^{v_1}|a,p^{v_2}|b$. If we suppose that there exist $v_1,v_2$ with them both being the largest integers such that $p^{v_1}|a, p^{v_2}|b$,  with $v_1+v_2= : v $ then $p^v|ab$. (I don't believe this to be a formal proof but rather my best own "idea" I can come up with...)  The script also mentions that the padic valuations' sums are bounded: $|x+y|_p\le \sup\{|x|_p,|y|_p\}$, how to show this?   Edit:   According to Robert Israel and Bill Dubuques answers, the first proposition is proven, if I understood correctly:   Given $ord(a)= v$ and $ord(b) = u$ which is the same as $a:= p^{v}m, b:= p^{u}n$ with $gcd(m,p)=gcd(n,p)=1$, because $ab=p^{u+v}mn$ with $gcd(mn,p)=1$ it follows that $ord(ab)=ord(a)+ord(b)$ and so $|xy|_{p}=p^{-ord(xy)}=p^{-(ord(x)+ord(y))}=|x|_{p}|y|_{p}$  Now to show: $|x+y|_{p}\le sup\{|x|_{p},|y|_{p} \}$  and the second can be tackled like this: set $a:=p^{v}m. b:=p^{u}n$, then checking two cases $1:(u=v)$ and $2:(v&lt;u)$: $(a+b)=p^{v}m+p^{u}n= p^{v}(m+p^{u-v}n)$ so in case of (u=v) it follows that  $ord(a+b)= u = sup\{ord(a),ord(b)\}$  and in case of $(v&lt;u)$ because the biggest v is $v:= u-1$: $ord(a+b)\le p^{u-1}(m+pn) \le p^{u}(m+n)= sup\{ord(a),ord(b)\}$  It seems that I did something wrong in both cases... I encountered a problem today to prove that $(X_n)$ with $X_n = \cos(n!)$ does not have a limit (when $n$ approaches infinity). I have no idea how to do it formally. Could someone help? The simpler the proof (by that I mean less complex theorems are used) the better. Thanks Claim: Let $X$ be a metric space. If $A,B\in X$ are disjoint, if A is compact, and if B is closed, then $\exists \delta&gt;0: |\alpha-\beta|\geq\delta\;\;\;\forall\alpha\in A,\beta\in B$.  Proof. Assume the contrary. Let $\alpha_n\in A,\beta_n\in B$ be chosen such that $|\alpha_n-\beta_n|\rightarrow0$ as $n\rightarrow \infty$.  Since A is compact, there exists a convergent subsequence of $\alpha_n\;(n\in\mathbb{N})$, $\alpha_{n_m}\;(m\in\mathbb{N})$, which converges to $\alpha\in A$.  We have   $$|\alpha-\beta_{n_m}|\leq|\alpha-\alpha_{n_m}|+|\alpha_{n_m}-\beta_{n_m}|\rightarrow0 \;\;\;as\;\;m\rightarrow\infty.$$ Hence $\alpha$ is a limit point of B and since B is closed $\alpha\in B$, contradiction.  Is my proof correct? I feel as though I am missing something simple which would trivialize the proof. Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$ $(a)$ Find all rational points on the circle $x^2 + y^2 = 3$, if there are any. If there is none, prove so.  $(b)$ Find all rational points on the circle $x^2 + y^2 = 17$, if there are any. If there is none, prove so.  I'm not sure how proceed with finding a general formula (if there is one)  I know that for $(a)$ there is no rational points but I don't know how to explain that there are none.   whereas for $(b)$ there are such points, $(1,4)$ for example. I think that we can find the intersection between the line $y=m(x-1)+4$ and $x^2 + y^2 = 17$  Any help is appreciated! Here's Prob. 3, Chap. 3 in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition:      If $s_1 = \sqrt{2}$, and $$s_{n+1} = \sqrt{2 + \sqrt{s_n}} \ \ (n = 1, 2, 3, \ldots),$$ prove that $\left\{ s_n \right\}$ converges, and that $s_n &lt; 2$ for $n = 1, 2, 3, \ldots$.    My effort:   We can show that $\sqrt{2} \leq s_n \leq 2$ for all $n = 1, 2, 3, \ldots$. [Am I right?]  Then we can also show that $s_n &lt; s_{n+1}$ for all $n = 1, 2, 3, \ldots$. [Am I right?]  But how to calculate the exact value of the limit? Where does this sequence occur in applications? Gel circular polarising filter I am contemplating buying a lens that only takes rear gel filters. Is it possible to buy a circular polarising filter in gel format? If so, who can supply them (preferably UK based)? Let $a, b, c \in \mathbb{N}$. Show that if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.  Using basic divisibility criteria I couldn't advance anything. How can one expand the function $f_1(x) = x$ on $(−π, π)$in terms of the functions $\cos nx, n = 0, 1, 2, ...$ and $\sin nx, n = 1, 2, ...,$ in a way so that $$f_2(x) = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$$ is the expansion of the $f_1$, how is that? I have asked  related to the same issue but didn't get full answer, I have been told that this is a standard application of Fourier series, $f_1$ and $f_2$ are equivalent in the sense that $f_1(x)=f_2(x)$ for all $x∈(−π,π)$. For any $x$ in this interval, the Fourier series will converge to $f(x)$, but I didn't get any rigorous proof  with elaborate explanation. So, plz provide rigorous proof of $f_1=f_2$ with elaborate explanation as I am new to the subject. Thanks You. I have attached the excerpt below -