If the children know their math they could move on to the next step and say, "Yeah? Well, I have 2 to the power of infinity!" 2^infinity has a higher cardinality than simply infinity (usually defined as all real numbers or rational numbers). At this point things get ridiculous (if they haven't already) because there will always be a larger set (the power set), even if you took 2 to the power of infinity an infinite number of times there would still be a larger set. The diagonal argument shows how this is true.
Think about it: if some kid had an infinite number of Lego's, it would create a black hole from the massive gravitational force. Whoa.