One to the power of zero

Before, I had never paid attention to the strange equality - one to the power of zero is equal to one to the power of one. Any number to the power of zero is equal to one. Any number to the first power is equal to the same number. If the number is equal to one, then a strange equality results.

Оne to the power of zero

In the process of studying number theory, I got to a place where the generally accepted option of raising one to the zero power violates the logic of certain rules. The logically correct result is obtained if one to the power of zero is equal to zero.

Оne to the power of zero

The introduction of one condition into the general rules led to a change in many obvious statements, which without this condition would not raise any doubts. Why am I being so cruel to mathematics? For the sake of a result that is the logical conclusion of the area of dissemination of general rules. The deeper I dive into the unknown, the more new and interesting I find. This situation makes it very difficult to finish work on something that seemed simple and understandable just yesterday.

I know very little mathematics, which is not interesting to me. Do you know the branches of mathematics in which one to the power of zero is equal to zero?