A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Show that \[[x]+[x+\frac{1}{2}]=[2x]\]
where \[[x]\] is the greatest integer of x
anonymous
 one year ago
Show that \[[x]+[x+\frac{1}{2}]=[2x]\] where \[[x]\] is the greatest integer of x

This Question is Open

perl
 one year ago
Best ResponseYou've already chosen the best response.0You can consider cases. When x is an integer, when x is not an integer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@perl Would you please help me out

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Here's a way you can solve this that I just came up with so I don't know if there's an easier way. First let's define \(0 \le d<\frac{1}{2}\) Then this means we can reach all numbers as either: \(x=n+d\) or \(x=n+d+\frac{1}{2}\). Why these weird choices? Cause when we plug them in we know no matter what \(d\) is we have: \[[n+d] = n\] \[[n+d+\frac{1}{2}] = n+1\] So we have two separate cases, plugging 'em in to: \[[x]+[x+\frac{1}{2}]=[2x]\] I think that will end up working?

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.0"empty' give the answer i give another way you can also take two case below and check both of them \[\lfloor x \rfloor =2n\\ \lfloor x \rfloor=2n+1\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.