+0  
 
+1
245
1
avatar

\(\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor\)

Guest Apr 29, 2017
 #1
avatar+92781 
+1

\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor

 

\(\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor \)

 

firstly

\(\left| x - \left| x-1 \right| \right| \ge 0\qquad \text{because it is an absolute value}\\ so \;\;\;\lfloor x \rfloor \ge0\\ \therefore\quad x\ge0 \)

 

so

\(\left| x - ( x-1 ) \right| = \lfloor x \rfloor\\ \left| x - x+1 \right| = \lfloor x \rfloor\\ 1 = \lfloor x \rfloor\\ 1\le x<2\)

Melody  Apr 29, 2017
edited by Melody  Apr 29, 2017
edited by Melody  Apr 29, 2017

11 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.