Approaching to Zero at a Speed
If N --> 0 is faster than m --> 0, N^m --> 0^m = 0.
Then 0^0 = 0.
On the other hand, if N --> 0 is slower than m --> 0,
N^m --> N^0 = 1.
Then 0^0 = 1.
As for multiplication,
N x 0 = 0, while N is any given number.
Then, N = 0/0.
Accordingly zero divided by zero is not constant, as N = 1, 2, 3, ..., N.
However, regarding m/N,
If N --> 0 is faster than m --> 0, m/N --> m/0.
Then 0/0 = infinity.
If N --> 0 is slower than m --> 0, m/N --> 0/N.
Then 0/0 = 0.
But what if both N and m approaches zero at the same speed? Maybe N has a higher priority than m in the case of N^m, but m might have a higher priority than N in the case of m/N.
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Mar 2:22 And no man putteth new wine into old bottles: else the new wine doth burst the bottles, and the wine is spilled, and the bottles will be marred: but new wine must be put into new bottles.