Date: Sat, 6 Jan 2001 15:25:05 +0200 (IST)
From: Sasha Goldshtein
When introduced to a^k = a*a*...*a k times you are also introduced to the basic rules of exponential arithmetic: (a^m) * (a^n) = a^(m+n). Since we would like to maintain the rules for all exponential identities with real exponents, it is necessary to maintain that a^0 = a^(n-n) = a^n * a^(-n) = (a^n) * 1/(a^n) = a^n/a^n = 1. Certainly, the definition could have skipped 0 - but from there you can derive a set of rules which, although will not probably result in a contradiction, but will not resemble the exponential real-number arithmetic that we know.
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