Originally Posted by
kathrynmath Limit only at the even numbers?
if 1<x<2, [x]=1 Then f(x)=x-2. The limit=0
If 2<x<3 [x]=2 Then f(x)=x-2 The limit =0
a-1<x<a where a is an odd number. [x]=a-1. Then f(x)=x-(a-1). Limit as x goes to a=1
a<x<a+1 where a is an odd number. [x]=a. Then f(x)=x-(a-1+1). Limit as x goes to a= 0
a-1<x<a where a is an even number. [x]=a-1. Then f(x)=x-(a-1+1). Limit=0
a<x<a+1 where a is an even number. [x]=a. Then f(x)=x-a. Limit = 0
So the limit exists for even numbers, it seems.