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:

$latex \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= 2$

1. Take f = log for Mapping:

$latex \log\sqrt{2}^{\sqrt{2}^{\sqrt{2}}} $

$latex = \sqrt{2}\log\sqrt{2}^{\sqrt{2}}$

$latex = \sqrt{2}\sqrt{2}\log\sqrt{2} $

$latex = 2\log\sqrt{2} $

$latex = \log (\sqrt{2})^2 $

$latex = \log 2$

2. Inverse of log (bijective):

$latex \log \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= \log 2$

$latex \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= 2$