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### Zero divided by zero

Calculating with zero can be very confusing. However, it is always logical.

##### Explanation

We start with a simple division

This calculation is correct. We now take 0, and write

This calculation is wrong, because the correct answer is indeterminate. And because 0^{0} ≝ 1, it applies

That seems absurd. *Where is the error exactly?* Dividing by zero is not allowed. You see it directly in the task itself. Further calculations make no sense. The notation 0^{–1} is also wrong.

The calculation of has two answers and is indeterminate.

For 7^{0} = 1 the calculation was correct. It is defined *by definition* that 0^{0} ≝ 1, because you cannot calculate it. But that is actually logical.