I found lots of references that say, "the probability that a continuous random variable equals some single value is always zero". Why is that?  Here is a counterexample I thought of: supposing $X\sim N(0,1)$, define $Y=min(X,0)$. Then Y is a continuous random variable but the probability of $Y$ at a single point $0$ should be $0.5$, not zero.  Also, I think any CDF would be left continuous if "the probability that a continuous random variable equals some single value is always zero".  What is wrong with my thoughts?   P.S. Examples of the references are:
I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ?
Is there any text editor which supports Markdown (Ask Ubuntu's formatting style)? Simple Smart Phone detection Set a polygon's normal's orientation as the objects local rotation orientation (if every polygon is an object) NPN circuit to switch 12v 1A DC load by 3.3v 1A DC using PIR Does deleting iCloud photos affect them on devices? If I delete a photo from my iCloud will it also be removed from my devices that are connected to my account? Let's say I'm running a simple server and have accept()ed a connection from a client.  What is the best way to tell when the client has disconnected? Normally, a client is supposed to send a close command, but what if it disconnects manually or loses network connection altogether? How can the server detect or handle this? Combining the entries of two lists Algorithms for automatic model selection I would like to implement an algorithm for automatic model selection.  I am thinking of doing stepwise regression but anything will do (it has to be based on linear regressions though).   My problem is that I am unable to find a methodology, or an open source implementation (I am woking in java). The methodology I have in mind would be something like:   calculate the correlation matrix of all the factors pick the factors that have a low correlation to each other remove the factors that have a low t-stat add other factors (still based on the low correlation factor found in 2.). reiterate several times until some criterion (e.g AIC) is over a certain threshold or cannot or we can't find a larger value.   I realize there is an R implementation for this (stepAIC), but I find the code quite hard to understand. Also I have not been able to find articles describing the stepwise regression. Entries I can safely exclude doing backups Is the gravitational constant $G$ a fundamental universal constant? Group algebra ever a field? Let $G$ be a group. 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Are there any good C++ decompilers out there?  I've already ran across . I've got an HP Pavilion Touchsmart notebook that came with Windows 8. I've upgraded to 8.1, and now I want to dual-boot an Ubuntu distribution with Windows 10. When dual-booting with Windows 8.1, the Windows Boot Manager always took priority, even after installing GRUB. What do I need to do to get GRUB to be the default bootloader instead of Windows Boot Manager? Maximum number of files being uploaded by input type file access parent object in javascript How Special Relativity causes magnetism I'm looking for some help disproving an answer provided on a  I posted about computing the number of double square combinations for a given integer.    The original question is from the Facebook Hacker Cup       Source: Facebook Hacker Cup   Qualification Round 2011      A double-square number is an integer $X$   which can be expressed as the sum of   two perfect squares. 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Knowing this, writing a program which   gives the number of solutions is easy:   compute prime numbers up to $46341$ once   and for all.      Given $k$, compute the prime divisors of   $k$ by using the above list (test up to   $\sqrt{k}$). Count the ones which are   equal to $1 \bmod 4$, and sum. Multiply   answer by $4$.   When I go through this algorithm for $25$, I get $8$ which is not correct.          For each prime factor (pf) of $25$ ($5$, $5$ are prime factors of $25$)         if pf % $4$ = $1$ (true for both $5$'s), add $1$ to count      return $4$ * count (count would be $2$ here).          So for $25$, this would be $8$ How can I tell if two Minecraft mods are compatible? If I want to use two mods together, e.g.  and  (which don't state compatibility with one another), how can I tell if they will work together (and not break Minecraft - forcing me to re-download a fresh copy)? List creation/manipulation