Saturday, February 22, 2014

"new wine must be put into new bottles" - Approaching to Zero at a Speed


A Tokyo Downtown Street


Approaching to Zero at a Speed

Regrading N^m,
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.