One Sided Limits of Greatest Integer Function

[aliasadullahb]

Can somebody tell me how to find one sided limits for greatest integer function, say Lim x->n-, [[x/2]]. that is limit x approaches n from left of [[x/2]] where [[]] represent greatest integer function and n is any integer.

I know how to find one sided limits for simple [[x]].

 

[mathman]

If n is even, the limit is n/2. If n is odd, the limit is (n-1)/2.

 

[chiro]

The technical way is to use the epsilon-delta proof to show that you get all the properties for some delta and epsilon and so on.

Since the function is continuous in-between the values of the integer points for these types of functions (floor, ceil, etc) then you can use math-man's answers provided above.