What is the Infimum of the Set of Rational Numbers with respect to pi?

[muso07]

Homework Statement

Find inf{|x-pi|:x\inQ}

Homework Equations

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. :)

 

[HallsofIvy]

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.

 

[muso07]

Thanks for the clarification. :)