As part of a social science text, in one place I need to write fractions like 1/2, 1/4, 1/3. How can I write these fractions in an elegant way without using mathematical packages?
I know I've seen somewhere how to typeset 1/2 as ½, but with arbitrary fractions (that is, a macro that takes two arguments and makes the first denominator and the second numerator...). Now I can't seem to find it.  How do I typeset an arbitrary fraction the same way as ½?
What is the difference between a predicate and function? I need to to understand the difference between predicates and functions in the context of Clasual Form Logic in order to define the Herbrand universe.  If I have p(x) :- q(f(x)) would I be right in saying that p and q are predicates while f is a function because it is "nested"?  By this thinking then if I have p(x) :- q(x) both p and q are predicates and I have no functions?  If this is incorrect then how can I tell the difference between a predicate and function? database disk image is malformed with dnf on Fedora 29 Is a business card necessary for a graduate student? I know some PhD students have their own business cards, but I don't know if it is a standard practice for PhD students to have their own business cards. I think a business card can be useful for networking in conference or collaborating with some industrial partners. So, is are business cards necessary for a PhD student or other graduate students attending conferences?   PS: in case it is field-specific, I would like to know the different practices in different fields Why does the checkbox stay checked when reloading the page? Is it ok to use an alternate account while my main user is restricted? I'm new to Stack Exchange, and my main user only has 16+ rep. And it's been blocked in Code Review. I need to use Code Review today. Should I use an alternate account? In some scenes in Avengers: Age of Ultron Iron man, War Machine, and Captain America try to lift Thor’s hammer but they end up failing. At some point Vision lifts it easily. How can Vision lift it? How do I disable touchpad when using a mouse Let $x &gt; 1$ and $a$, $b$ be positive integers. I know that $a$ divides $b$ implies that $x^a - 1$ divides $x^b - 1$. If $b = qa$, then  $$x^b - 1 = (x^a)^q - 1^q = (x^a - 1)((x^a)^{q-1} + \ldots + x^a + 1).$$  I'm interested in the converse of the statement. If $x^a - 1$ divides $x^b - 1$, does this imply that $a$ divides $b$? MySQL INT meaning Why do we use the simple past but not the present or future in the following expressions:  Don't you think it's time we went a little further Don't you think it's time we ate Don't you think it's time we went home What *is* an Artificial Neural Network? Identifying genes from a list of genes What is the differance between Linked and Appended data from external .blend files? Determining the name of the VMware host of a VM guest - from the guest I am trying to get Juju working on Windows 8 but I am running in to some errors when trying to get juju to see my ssh keys:  C:\Users\username&gt; juju bootstrap error: error parsing environment "azure":     read C:\Users\user\SkyDrive\Documents\Azure\ssh\: The handle is invalid.   I've added a public key I generated with putty to the directory above called azure  My environments.yaml file has this in it:  authorized-keys-path: C:\Users\user\SkyDrive\Documents\Azure\ssh\   Any ideas? So I'm getting my listItems with a Camlquery, but i want to calculate the avg of the "price" rows  This is the code I've used so far:  function VisaLista() {     namn = document.getElementById("txtNamn");     var camlQuery = new SP.CamlQuery();     camlQuery.set_viewXml(     "&lt;Where&gt;" +     "&lt;And&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Title'/&gt;&lt;Value Type='Text'&gt;" + namn + "&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;Or&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Prioritet'/&gt;&lt;Value Type='Text'&gt;Hög&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Status'/&gt;&lt;Value Type='Text'&gt;Startad&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;/Or&gt;" +     "&lt;/And&gt;" +     "&lt;/Where&gt;");     listItems1 = list.getItems(camlQuery);     clientContext.load(listItems1);     clientContext.executeQueryAsync(OnSuccessVisa, OnFail); } function OnSuccessVisa() {     var listEnumerator = listItems1.getEnumerator();     var elmt = 0;     while (listEnumerator.moveNext()) {         var currentItem = listEnumerator.get_current();         elmt = (currentItem.get_item('_x0072_zb6'));          var sum = 0;         for (var i = 0; i &lt; elmt.length; i++) {             sum += parseInt(elmt[i], 10);         }          var avg = sum / elmt.length;          document.write("The sum of all the elements is: " + sum + " The average is: " + avg);     }     $("#Kategori1").text = "Medelvärdet för dessa ordrar: " + avg }   I am getting following error     "Cannot get the value length of null - at elmt, line 43 Website display problem - across all browsers whenever I go to  or  the page loads like this:    How can I fix this? How to keep application running after closing the terminal? Is "reserved" an adjective or verb in this example? I need an answer about this sentence please:     We had a reserved seat.   Reserved in this sentence is a verb. I read that in a morphology book.  My question is: how does this become a verb?  I thought it was an adjective. JavaScript 64 bit numeric precision Is there a way to represent a number with higher than 53-bit precision in JavaScript? In other words, is there a way to represent 64-bit precision number?  I am trying to implement some logic in which each bit of a 64-bit number represents something. I lose the lower significant bits when I try to set bits higher than 2^53.  Math.pow(2,53) + Math.pow(2,0) == Math.pow(2,53)   Is there a way to implement a custom library or something to achieve this?