Question: Prove that $\mathbb{Q}$ under addition is not isomorphic to  $\mathbb{R^{+}}$ under multiplication.   I wonder what is a good way to approach this? Would constructing a map be more helpful?  Thank in advance. Hints only*
To show: $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$  Now, the equation $x^{2} =3$ has a solution in $\mathbb{R}$, but not in $\mathbb{Q}$.  Hence they are not isomorphic to each other.  Is that right, or do I need to prove something else?  Thanks.
Can I get more than 1000 records from a DirectorySearcher? I just noticed that the return list for results is limited to 1000. I have more than 1000 groups in my domain (HUGE domain). How can I get more than 1000 records? Can I start at a later record? Can I cut it up into multiple searches?  Here is my query:  DirectoryEntry dirEnt = new DirectoryEntry("LDAP://dhuba1kwtn004"); string[] loadProps = new string[] { "cn", "samaccountname", "name", "distinguishedname" }; DirectorySearcher srch = new DirectorySearcher(dirEnt, "(objectClass=Group)", loadProps); var results = srch.FindAll();   I have tried to set srch.SizeLimit = 2000;, but that doesn't seem to work. Any ideas? What program can be used to package software into one executable? I need to package an application into a single executable file (so that I don't have to install it, so that it will be portable).  Does anybody know what I can use to make a program portable? What is the meaning of this two letter code in the YouTube logo? I see a new logo with CA at youtube.com. Does anyone know what it means? What five odd integers have a sum of $30$? #!/bin/bash - no such file or directory What does the term "BODMAS" mean? What is BODMAS and why is it useful in programming? Make Windows 10 stop installing driver software automatically Sometimes when I write, for example, "the boundaries of segments", I am suggested to use "segments' boundaries" or even "segment boundaries".   Or "the page's content" vs. "the content of the page" vs. "the page content". Then I would like to know is it always preferred to use phrases with apostrophe or adjective?  For example      In our terms, they are mainly textual elements within the page content, which serve as the starting point  of a data region (or a data region's starting point ?)  or a distinctive feature within it Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $ If $x&gt;0$, $y&gt;0$, $z&gt;0$ and $x+y+z=6$ then find the minimum value of    $$ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $$   Thanks in advance. Why does the amount of energy transferred depend on distance rather than time? The change in energy of an object can be determined by the work equation, where work is the change in energy:  $$ W = F \cdot d $$  I conceptualize the transfer of energy as simply a series of small "packets" of energy being transferred at every Planck length. These small "packets" of energy add up to the total energy transferred (i.e. work). I'm not sure if this conceptualization is correct, so correct me if I am wrong.  However, it makes me wonder why the amount of energy transferred is dependent on distance and not time.  $$ m_1 = 10~kg \\ m_2 = 20~kg \\ W_1 = (10~N)\cdot(5~m) = 50~J \\ W_2 = (10~N)\cdot(5~m) = 50~J \\ W_1 = W_2 \\ t_1 \neq t_2 $$  If I apply a constant force on an object, why isn't the energy transferred at a constant rate with respect to time? The energy transfer rate varies dependent on how long it takes to cover the set distance.  In other words: why is the energy transferred consistent per unit of distance, and not per unit of time? First week of August in Scotland : What kind of clothes to pack? In a couple of weeks I will be going to Edinburgh, Scotland. I've been told that the weather is very unpredictable throughout the year. Can you suggest what I should pack as regards clothes? That's really embarrassing, however I need to ask it. I could not prove that the normed space    $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle $ is complete (as a metric space), where $\| f\|_1 = \int_0^1 |f(x)|dx$. I don't really know how to explicit a continuous functions as a limit of a Cauchy sequence. I tried to prove that the pointwise limit (of the Cauchy sequence) have just a finite number of discontinuities (I don't know if it's true) and then approximate it by a continuous function.  Thanks in advance. Why cant I navigate to lightning component in communities? Im on a lightning community, i have a lightning component and i want to open another component with this code:  navigateToMyComponent : function(component, event, helper) {     console.log('1');     var evt = $A.get("e.force:navigateToComponent");     console.log('2');     evt.setParams({         componentDef : "c:CompetenciaComponent"     });     console.log('3');     evt.fire();     console.log('4'); }   this its the console log:   NOTHINGS HAPPEND AND I DONT KNOW WHY I have a NetGear WGR614 wireless router.  There is a 'region' setting in the wireless options.  I'm wondering what technical purpose of this setting is?  The admin help states:     It may not be legal to operate the router in a region other than the region shown here.    Which makes me wonder if it could be adjusting it's max power output based on regional radio laws? How can I disable the drag handle on the desktop? Why do the directories /home, /usr, /var, etc. all have the same inode number (2)? Movement arrow in gloss Can I have multiple primary keys in a single table? Can I have multiple primary keys in a single table? I'm building a Core  system which supports dual-channel memory (up to 16&nbsp;GB in four DIMMs), my target is 8&nbsp;GB. From the performance perspective, is it better to have two times 4&nbsp;GB or four times 2&nbsp;GB? Adding Layer Files (.lyr, .lyrx) to QGIS At college we use ArcGIS Desktop 10, but that does not function on my Mac so I have QGIS there instead.  I want to do my exercises with QGIS, but in ArcGIS Desktop we use .lyr files with ArcMap and .lyrx files with ArcGIS Pro, and they are not supported by QGIS.  Does anyone know, how I can connect the *.lyr files to my *.shp files to use them on my Mac with QGIS?