Hmm..interesting to see mathematicians at Sajha. Here is a proof I want you guys to do without searching anywhere...shshsh..dont cheat... Prove that as 0.999999 tends to infinity, it tends to infinity. It is pretty simple actually. Prove that Sqrt of 2 is irrational. This one is a bit tricky though. Hint: Try to work the opposite way or in other words, prove that Sqrt 2 cannot be rational and if it cannot be rational, it has to be irrational. Good luck!!! PS: First one to give the correct answers to both will get a cash prize of $100 on April 1st.