# Interesting (and funny) exercise

• Oct 6th 2010, 06:12 AM
eurialo
Interesting (and funny) exercise
Imagine you are in $\mathbb{R}^2$ with the euclidean topology. You have a family of rectangles with the property that at least one of its side has an integer length (the other may be any real number). Prove that if we arrange those rectangles to form another bigger rectangle, it still has this property.
• Oct 6th 2010, 06:39 AM
Defunkt
I think I posted this a few months back; I'll try to search for it..
It is indeed a nice exercise.

EDIT: There we go..
http://www.mathhelpforum.com/math-he...les-99826.html
• Oct 6th 2010, 06:45 AM
MathoMan
If such a family of rectangles could be thought of as a $\sigma$-algebra in $\mathbb{R}^2$ then it would be obvious, right?!