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Infinity to the power of zero

According to current mathematic theories, infinity to the power of zero is

0 = ?



For every number applies a0 = 1. However, infinity is not a number (it has no fixed value), and you must always pay attention with the number 0. We start with

and write this as

The exponent may become very small, the result remains always . Therefore, we simply write

as Δx is infinitely small, but it is not zero. Sorry, this is not what we are looking for. The exponent should be 0. We try it in another way, and write

Now a approaches infinity, but it is still a number. The correct answer apparently is

0 = 1          

Is this correct or not? Well, according the actual mathematic theories it is undefined.


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