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0x is unambiguously equal to zero everywhere except at x=0. It may seem odd then to define 00 as one since that makes 0x discontinuous but looking at the function y^x as y approaches zero one sees that such a discontinuous function is exactly what should be expected. This can be clearly seen in the image below. The four lines are 0.1x, 0.01x, 0.001x, and 0.0001x.

0^x

See also

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