# Homework Help: Infimum homework problem

1. Mar 4, 2010

### muso07

1. The problem statement, all variables and given/known data
Find inf{|x-pi|:x$$\in$$Q}

2. Relevant equations

3. The attempt at a solution
I was thinking that the greatest lower bound must be 0, but that seemed a bit simple. Is there any justification I have to give for this?

Any help would be much appreciated. Cheers. :)

2. Mar 4, 2010

### HallsofIvy

Re: Infimum

Yes, there exist rational number arbitrarily close to any real number and, in particular, arbitrarily close to $\pi$. The infimum of $|x- \pi|$ for x rational is 0.

3. Mar 4, 2010

### muso07

Re: Infimum

Thanks for the clarification. :)