I have old 32-bit hardware. I want to install ubuntu 18.04 mini iso without internet because my LAN card not working so does anyone know how to install mini ISO offline thanks.
Why is there no 32 bit ISO for the new Ubuntu 18.04?
Gave up waiting for root device on Ubuntu Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists ? If it does then what is the value ?   I don't think even L'Hospital's rule can be applied . Please help . Thanks in advance Deleted comments leave badge on iOS app When someone leaves a comment that involves you being notified, you get the notification both on the main toolbar on Stack Exchange and as a notification/badge on the iOS app.  If you read a comment on the website and cause the notification to be removed from the toolbar, the badge also gets removed from the iOS app.  However, when a comment that has previously caused a notification/badge to appear on iOS gets deleted, the badge remains on the iOS app while the notification gets removed from the website toolbar.  Could the badge also be removed from the iOS app in this situation? Delta-like symbol in LaTeX I'd like to write a majuscule delta-like symbol in LaTeX but I can't find it's syntax anywhere. You can see the symbol on equation (12) of the following paper:  "". Pluralizing abbreviations where the noun is not the last word For abbreviations - both acronyms and initialisms - where the last word in the abbreviation is the noun, I'm accustomed to adding an 's' with no apostrophe (e.g. ATMs), as described in the answer to this question:   But how do you pluralize abbreviations where the noun is not the last word? E.g. 'Point of Presence' (POP)  I can see how 'POPs' could read 'Point of Presences', when the intention is 'Points of Presence.' How can there be animals on the surface in Zion's world? It is apparently canon that  in Neo's day.  However, in the first movie, The Matrix, Morpheus tells Neo that one of the things known for certain is that humans "burned the sky" in order to deny solar engery to the machines, which in turn led to the humans who survived the War being plugged into the Matrix to provide bioelectric energy to supply the machines.  If there's not enough sunlight for solar power, how can there be enough to grow plants to serve as food for animals?  Low levels I can understand -- house plants, at least, thrive in conditions too dim for solar panels to produce cost-effective power -- but every surface scene we see in the trilogy is as dark as a cloudy night; light coming only from the machines.  That wouldn't begin to support photosynthesis, which means all animal life would starve in, at most, a matter of a few years. Why did Palpatine wait so long before giving Order 66? C# Change A Button's Background Color zsh scripting - How do I NOT match a pattern in filename generation? I install virtualBox on Ubuntu 16.04, but after install and create new virtual Host shows this error:     Kernel driver not installed (rc=-1908)      The VirtualBox Linux kernel driver (vboxdrv) is either not loaded or there is a permission problem with /dev/vboxdrv. Please install virtualbox-dkms package and load the kernel module by executing  modprobe vboxdrv       as root. If it is available in your distribution, you should install the     DKMS package first. This package keeps track of Linux kernel changes and   recompiles the vboxdrv kernel module if necessary.  where: suplibOsInit what: 3 VERR_VM_DRIVER_NOT_INSTALLED (-1908) - The support driver is not installed. On linux, open returned ENOENT.     How to address this modprobe vboxdrv error? Compact topological space with closed graph implies continuity Let $X,Y$ be topological spaces and $f:X \rightarrow Y$  If $Y$ is compact and $G(f)$ (graph of $f$) is closed, show that $f$ is continuous.   I consider an open set in $X$, and as $G(f)$ is closed, $(X \times Y)-G(f)$ is open. And I guess I need to do something here. Then I can get some open sets. Also, I notice that compact is something relate to "finite". I guess I can use the compactness to do finite intersection or union and get the result finally.  But what should I do in the middle or I am not even on a right track. I can't seem to get Python to import a module in a subfolder. I get the error when I try to create an instance of the class from the imported module, but the import itself succeeds. Here is my directory structure:  Server     -server.py     -Models         --user.py   Here's the contents of server.py:  from sys import path from os import getcwd path.append(getcwd() + "\\models") #Yes, i'm on windows print path import user  u=user.User() #error on this line   And user.py:  class User(Entity):     using_options(tablename='users')      username = Field(String(15))     password = Field(String(64))     email    = Field(String(50))     status   = Field(Integer)     created  = Field(DateTime)   The error is: AttributeError: 'module' object has no attribute 'User' Interior of cartesian product is cartesian product of interiors I have to prove that:  $$Int(A\times B) = Int(A)\times Int(B)$$  Where $A\subset M$ and $B\subset N$, both $M$ and $N$ metric spaces.  The problem is that the exercise does not specify the metric, so I need to try to prove it using a generic metric.  If $x\in Int(A\times B)$, then an open ball can be centered at $(x,y)$ such that it is contained in $A\times B$. Therefore, this open ball, $B((x,y),r)\subset A\times B$. It means that $d((x,y),a)&lt;r$ for any $a\in A\times B$ for some $r&gt;0$. I guess that if I can take from here that $d(x,a)&lt;r$ and $d(y,a)&lt;r$ I can prove thhat $Int(A\times B)\subset Int(A)\times Int(B)$, but I still have to prove the other way around.   Any ideas? Triangle Inequality question with fractions Given $a, b \in \mathbb{R}$, prove that   $$\frac{|a + b|}{1 + |a + b|} \le \frac{|a|}{1 + |a|} + \frac{|b|}{1+|b|}$$  When does equality hold?  The only useful thing I could get (using the triangle inequality) is:  $$\begin{align}1 + \left|\left(a + \frac{ab}{2}\right) + \left(b - \frac{ab}{2}\right)\right| &amp;\le 1 + \left|a + \frac{ab}{2}\right| + \left|b - \frac{ab}{2}\right|\\ &amp;\le 1 + |a| + |b| + |ab|\\ &amp;=(1 + |a|)(1 + |b|)\end{align}$$  But it seems to be inapplicable! Any ideas? How can I encrypt and decrypt a string in C#? Electron Flow Confusion Using conventional notation in the diagram below, I understand that the circuit is not complete because the diode is in reverse bias. But knowing that the electrons actually flow from the negative to the positive terminal(direction of the arrows), wouldn't the electrons take a path from the negative terminal of the battery, go through the lamp and stop at the diode(the red path in the picture). If they would, then why doesn't the lamp light up with the first electrons that are able to flow through it before the voltage in the wire is built up and the current stops. Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$ I'm just wondering the reason behind being able to do this:  $$\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$$  Is there an elementary proof to the reasoning behind this? Questions on "All Horse are the Same Color" Proof by Complete Induction I'm bugged by the following that's summarized on p. 109 of .     False theorem: All horses are the same color.      Proof by induction:      $\fbox{$P(n)$ is the statement: In every set of horses of size $n$, all $n$ horses are the same color.}$   $\fbox{Base Case or $P(1)$:}$ One horse is the same color as itself. This is true by inspection.   $\fbox{Induction Step:}$ Assume $P(k)$ for some $k \geq 1$.   $\fbox{Proof of $P(k + 1) :$}$   Since $\{H_1, H_2, ... , H_n\}$ is a set of $n$ horses, the induction hypothesis applies to this set. Thus, all the horses in this set are the same color.   Since $\{H_2, H_3, ... , H_{n+1}\}$ is also a set of $n$ horses, the induction step likewise holds for this set. Thus, all the horses in this set are the same color too.         Therefore, all $n +1$ horses in $\{H_1, H_2, H_3, ... , H_n , H_{n+1}\}$ are the same color. QED.   The issue the instructor was trying to point out is clearly valid. For the case $n = 1$, there is only ${H_1}$. So this case says nothing about possible overlapping elements of each set of $(n + 1)$, for instance $H_2$ in the above proof.    But it was proposed in the class discussion that this was the only problem. Had you been able to prove $P(2)$ true, then a proof of the above format would have been fine.    My interpretation is that yes, you could prove all horses are the same color, if you can prove that any set of two horses will be the same color. But this format would not work.  Why not? The problem I see is that the above proof is for the existence of at least one particular pair of sets of horses of sizes $n$ and $n + 1$, such that in each set, all horses are the same color.  Particularly when the set of size $n$ is a subset of the set of size $n + 1$.  In order to prove the induction step, don't you need to prove that sets of sizes $n$ and $n + 1$, do not necessarily contain the same, overlapping elements?  You could prove that any horse can be added to a set of 2 horses.  Take the last two, and they must be the same color, and so on.  Wwhatever color the first two happen to be, all other horses must thus be the same color.    Am I misinterpreting the example, or am I making a logical error? Thanks in advance. How to get my actual data from ContentNote API in Salesforce using SOQL? Photo Map tip in QGIS 3 on windows