Toan: this is my try: a quarter can save a dollar in many cases at the vending machine. For example, we want a coke really bad while we only have two quarters in the pocket and the machine wants 75c for a coke.
@Toan: Right, we need a quarter for a cart at Aldi. I have not seen one at Fort Collins, but there is a singleton store , Sunflower, similar to Aldi.
@Tuyen: Chỗ đó thật khó giải thích :). Nhờ nó mà mình có cái chứng minh.
Too busy lately to check this blog but it seems (to me!) not much is going on. It’s a shame. 😦
If you want a more rigorous version of this then Banach-Tarski paradox is the one. Mathematically, you can be extremely rich or poor by just having a piece of gold. There is a nice exposition on this paradox by Ian Stuart in a 80’s Naturalist issue (as far as I remember).
Du’s proof is good for people who hate math and cannot pass College Algebra. Well, that’s how we popularize our stuff, right? 🙂
@Du: No I meant Ian Stuart at Warwick! I read his article long ago in order to explain the paradox to my daughter (I failed!). His article is for laymen and he did a good job (I didn’t). 😦
I believe that it’s hard to make Math (the real one) relevant to this real world. Either I’d try to cheat (myself) or be happy with my own world. Ask yourself: Is this world quantum or continuous? I hope that you will be happy and successful with your answer. I thought I was!