Zero Index

Zero Index Law

The zero index law states that anything (except zero) to the power of zero is 1.

a0 = 1, a ≠ 0

Q1) Should 00 = 1? Why?

Argument for YES

  1. In the fringe case of the binomial expansion of (a + 0)n , the first term will be an00 which implies that 00 has to be 1.

  2. When you consider the limit for xx as x tends to 0, the limit tends to 1.

Argument for NO

  1. When you consider the limit for 0x as x tends to 0, the limit tends to 0. Different approaches to 00 using different limits results in differing answers hence 00 is indeterminate.