「斑馬知識+挑戰」指數定律的證明

(A) When m and n are positive integers:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Doraemon1.jpg

(B) When m and n are negative integers:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Doraemon2.jpg

(C) When m and n are rational numbers:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Doraemon3.jpg

(D) When m and n are irrational numbers:
By the fact that irrational numbers can be written as sum of infinite numbers of rational numbers, for example:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Doraemon4.jpg

Then:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Mar08/Doraemon5.jpg

Finally the proof completes for all real numbers m and n.

又唔洗 complex 的, 條問題都冇問 :P
不過1同2係一樣的 (負數都係 real number), 你係咪問左多餘野?

2008-04-05 08:02:37 補充：
我對知識長這個 proof 有點微言....
因為呢個題目比較根本, 等我遲下寫返篇評論~

兄台，define exponential function over real/complex先啦。

你以為陶先生真係會係電視度解釋一條數？

2008-03-30 16:31:09 補充：
據我理解exponential function既定義根本就係佢list個條式，點證明定義啊？