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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
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This calculation is wrong, because the correct answer is indeterminate. And because 00 ≝ 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 70 = 1 the calculation was correct. It is defined by definition that 00 ≝ 1, because you cannot calculate it. But that is actually logical.