## Proof by Convergent Handwriting

Write the first line of your proof a units high. Write the next line of your proof a/2 units high. Then, write the next line a/4 units high. Continue the pattern, writing the nth line $a/2^{n-1}$ units high. What you’re doing is mathematical reasoning, and thus you’re being rational. The set of rationals is only countably infinite, so within the infinite number of statements you make, the proof of whatever you’re trying to prove is bound to arise somewhere.