The Oxford Interview

Haha. Not me lah. I would never ever apply to Oxford to study Math. It's not me. Haha. Anyway just remembered a question that was posed to Theen Yew at his Oxford Interview. Haha. This is the question:

Is 0.9999999999... (infinite terms) less than 1, more than 1 or equals to 1?

By answering this question, you could be on your way to Oxford! Wahaha. Apparently I think my dad's a genius. I asked him this question and he could get the answer! AMAZING!

The solution is so neat! I like it. Haha. Here it is:

You must recognise that 0.999999999... (infinite terms) forms a geometric progression.
i.e. 0.999999999...= 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + ...
                                 = 0.9 + (0.9 x 0.1) + (0.9 x 0.1^2) + (0.9 x 0.1^3) + (0.9 x 0.1^4)...
                                 = 0.9/(1 - 0.1)   [Formula for G.P. Sum to infinity]
                                 = 1
Therefore, 0.9999999... is equals to 1.

Alternatively, there's another proof:
i.e. 1/3 = 0.33333333... (infinite terms)
       0.99999999... = 0.3333333... x 3
                                = 1/3 x 3
                                = 1
Therefore, 0.9999999... is equals to 1.

Don't you think the proofs are elegant? Haha. That's the beauty of Math. =D

Anyway there's another proof which I can't remember. And there are more questions too! Haha. This is the only one I remember coz I'm teaching APGP now. Haha. Perfect. I shall post this question to my students tomorrow. Wahaha. 

Ok this is a random post. I just find this question quite interesting. This is the reason why I am a Math tutor now. LOL. =X