How is "point" in geometry undefined? I mean, when we say "A point in geometry is a location. It has no size, i.e., no width, no length, and no depth," is it not a definition?  If it is not a definition, then how can we know whether some statement is definition or not? What are the characteristics of a definition in math?
In Euclidean geometry texts, it is always mentioned that point is undefined, it can only be described. Consider the following definition: "A point is a mathematical object with no shape and size." I do not understand what is the problem with this definition. Please give the detailed reasons. Thanks in advance!
Down arrow button for choosing the desired site Why are certain example URLs like https://site.com/ and https://mysite.com/ blocked from post content? Why is  and  blocked from the post content on the main site? I tried to make a sample URL and I had to use  instead. I recall Asimov had a character who was The autoc of , clearly based on the word “autokrat” but I don’t recall the exact spelling.  This stumped Google, which would rather correct the spelling to some other word than find a unique word.  In the story, he had gone undercover and the reader did not know either that some other character was in fact the Autoc, until it had been revealed to the main character. Extruding Vector Files in Blender I am sure this has been discussed quite a few times, but I found a tutorial recently doing the exact same thing as I did, but in my case my logo is messing up!  Here is the link to the workflow:   This is what it looks like after adding the solidify modifier:   I already recalced the normals of my spline, but besides that it messes up my spline shape, it had no effect.  Any suggestions on how to fix it? How do I increase the render distance? I have created a simple model here   When rendering it the end of it is cut off   How can I get the camera to render a longer distance? Map matrix element to string How can I disable Alt-Scroll zoom in XFCE4 (Xubuntu) In XFCE4 desktop environments, alt+scroll wheel zooms my entire desktop. I'm finding this very annoying because sometimes I flick the scroll wheel to go to the top of a document then press the alt key for a some unrelated keyboard shortcut and find myself zoomed in so far I can't see anything at all. Is there any way to disable this feature? Sheet Specific Scripts I'm currently using the below script to timestamp when an edit is made to column 7 on a sheet named "Sheet 1".  function onEdit(e) {    if ([7].indexOf(e.range.columnStart) != -1) {    e.range.offset(0, 7).setValue(new Date()).setNumberFormat("dd.MM.yyyy at HH:mm");    }   }     I have a second sheet "Sheet 2" which I need to run the same script on but against column 5.  function onEdit(e) {    if ([5].indexOf(e.range.columnStart) != -1) {    e.range.offset(0, 7).setValue(new Date()).setNumberFormat("dd.MM.yyyy at HH:mm");    }   }     I've tried .getSheetByName("Sheet1") but just cant seem to get it working correctly. Reading and searching long man pages I finally got fed up when wanting to read about bash's read and it's -s option with man bash. I found the right spot eventually (around line 4500), but it was a frustrating as usual, since both /read and even /\s-s\s searches have way too many matches.  So, the question is: How can I read long man pages efficiently, or get same information in other ways, locally? As a specific example, how to reach the relevant documentation after seeing read -s pwd in a shell script? A good answer could be a shell script snippet, or hint about some tool and how it is used, or something else entirely, as long as it helps in finding the right spot to read.  Note: I'm not tagging with  because I want the question to be about man page reading in general, even though that quite possibly is the most commonly encountered humongous man page. Systems of equations with a single number In the top left corner of the post-race menu, there is a prompt to press + to add (or remove) one star out of six. What do these stars do? Is there a characterization of the nonconstant entire functions $f$ that satisfy $|f(z)|=1$ for all $|z|=1$?   Clearly, $f(z)=z^n$ works for all $n$. Also, it's not difficult to show that if $f$ is such an entire function, then $f$ must vanish somewhere inside the unit disk. What else can be said about those functions?  Thank you. Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$ When I press Ctrl+Alt+T the Terminal opens after around 30 seconds. That's pretty annoying. If I open it with Alt+F2 and enter gnome-terminal the window appears instantly as usual.  I'm using Ubuntu 16.04 with gnome3.  Thank you for your help in advance! I'm looking into a restful design and would like to use the HTTP methods (POST, GET, ...) and HTTP headers as much as possible. I already found out that the HTTP methods PUT and DELETE are not supported from the browser.  Now I'm looking to get different representations of the same resource and would like to do this by changing the Accept header of the request. Depending on this Accept header, the server can serve a different view on the same resource.  Problem is that I didn't find a way to tell my browser to change this header.   The &lt;a..&gt; tag has a , that can have a mime type, looked like a good candidate but the header was still the browser default (in Firefox it can be changed in about:config with the network.http.accept.default key). VARCHAR size limit in Excel spreadsheets Ridge & LASSO norms This post follows this one:   Here is my question:  As far as I know, ridge regularization uses a $\ell_2$-norm (euclidean distance). But why do we use the square of this norm ? (a direct application of $\ell_2$ would result with the square root of the sum of beta squared).  As a comparison, we don't do this for the LASSO, which uses a $\ell_1$-norm to regularize. But here it's the "real" $\ell_1$ norm (just sum of the square of the beta absolute values, and not square of this sum).  Can someone help me to clarify? From A Classical Introduction to Modern Number Theory by Ireland and Rosen, page 33:     Corollary 1 (Euler's Theorem). If $(a,m) = 1$, then $a^{\phi(m)} \equiv 1\,(m)$.      Proof. The units in $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. If $(a,m) = 1$, $\bar{a}$ is a unit. Thus $\bar{a}^{\phi(m)} = \bar{1}$ or $a^{\phi(m)} \equiv 1\,(m)$.   If I'm interpreting this correctly, this proof implicitly uses the fact(?) that if $G$ is a group and $x\in G$, then $x^{|G|}=1$, where $1$ is the identity element of $G$.  If this is indeed true, can someone explain why? (I have had no prior exposure to group theory.) How to reset the terminal properties and preferences? Should a student be penalized for using a theorem outside of the curriculum?