Zero to zero power

The fifth postulate of Euclid , in its usual version, tells us that a parallel and only one pass through a point outside a line . However, many geometers did not accept the independence of this postulate and some, including Gauss, Bolyai and Lobachevsky, formulated variants of this fundamental proposition, and in this way the so-called non-Euclidean geometries arose [1] .

Also, many elementary algebra texts indicate that 0 raised to 0 is undefined [2] ; however, it is possible to show that the null power of zero is zero is 1


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  • 1 Proposition
    • 1 Statement
    • 2 Test
  • 2 Limit equal to one
  • 3 References
  • 4 Bibliographic source



For a real number r, let g 0 be the function defined by the following [3] requirements:

r (0) = 1

r (t + 1) = r. g 0 (t) where (t = 0, 1, 2 …)


Obviously it is fulfilled

r (0) = 1

r (1) = r · g r (0) = r

r (2) = r · g r (1) = rr

r (3) = rg r (2) = rrr


The k-th power of r is named g r (k) and denoted g r (k) = r k

In this equality r is called the base and k the exponent of the power. As indicated, the definition is r 0 = 1 for every real number r.

In a special way

0 = 1

Limit equal to one

In mathematical analysis, when studying the exponential functions f (x) g (x) (the domain of f is a set of positive numbers), the limit of the transcendent elementary function y = x x , when x approaches 0 by On the right, the limit of y approaches 1. The L’Hôpital rule can be used to calculate the proposed limit.


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