Relationship-Mapping-Inverse (RMI)

Relationship-Mapping-Inverse (RMI)
(invented by Prof Xu Lizhi 徐利治 中国数学家 http://baike.baidu.com/view/6383.htm)

Find Z = a*b

By RMI Technique:
Let f Homomorphism: f(a*b) = f(a)+f(b)

Let f = log
log: R+ –> R
=> log (a*b) = log a + log b

1. Calculate log a (=X), log b (=Y)
2. X+Y = log (a*b)
3. Find Inverse log (a*b)
4. ANSWER: Z = a*b

Prove:

\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= 2

1. Take f = log for Mapping:
\log\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}
= \sqrt{2}\log\sqrt{2}^{\sqrt{2}}
= \sqrt{2}\sqrt{2}\log\sqrt{2}
= 2\log\sqrt{2}
= \log (\sqrt{2})^2
= \log 2

2. Inverse of log (bijective):
\log \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= \log 2
\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= 2

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