Zero, Constant or Variable
The number is a key to understanding how this universe was designed by God.
What is 0 to the power 0?
The problem is similar to that with division by zero. No value can be assigned to 0 to the power 0 without running into contradictions. Thus 0 to the power 0 is undefined
How could we define it? 0 to any positive power is 0, so 0 to the power 0 should be 0. But any positive number to the power 0 is 1, so 0 to the power 0 should be 1. We can't have it both ways.
Underlying this argument is the same idea as was used in the attempt to define 0 divided by 0. Consider a to the power b and ask what happens as a and b both approach 0. Depending on the precise way this happens the power may assume any value in the limit.They explain how any positive number to the power 0 gets 1 in the following way.
http://www.math.utah.edu/~pa/math/0to0.html
N^0 = N^(m-m) = N^m/N^m = 1
Specifically, if N = 2 and m = 3,
2^0 = 2^(3-3) = 2^3/2^3 = 8/8 = 1
So, it can be claimed that 0^0 = 0^(0-0) = 0^0/0^0 =1, no matter what value 0^0 has, since both the denominator and the numerator must have the same value 0^0, namely 0 to power 0.
But if 0 to power 0 is considered indefiniteness, 0^0 and 0^0 can have different values. The above tautology can be effective only if the value of 0^0 is constant.
In other approach, for example, 8 = 2+2+2+2 = 2^3, but 0 = 0, 0+0, 0+0+0, 0+0+0+0, etc. Therefore 0 = 0^1, 0^2, 0^3, 0^4, etc. Since 0 is indefiniteness, 0^0 must be also indefiniteness.
But we may think that 2^m means 1x2x2x2...x2.
If so, when m=3, 2^3 = 1x2x2x2 = 8. In this scheme, 2^0 = 1; 3^0 = 1; and N^0 = 1.
Even, 0^3 = 1x0x0x0 = 0. Then, 0^0 = 1.
Anyway, the number zero is essentially indefinite, since 0 = 0-0, 0-0-0, etc.
In contrast, 8/2 = 4, since 8-2-2-2-2 = 0 definitely.
But 0/0 = indefinite; if 0-0 =0, then 0/0 = 1; if 0-0-0 = 0, then 0/0 = 2, and so on.
You can subtract 0 from 0 any times.
So, we may well think that it is one that is the basis of the number system. With one, only zero has meaning arithmetically. Then we might have to think as follows:
0^3 = 1x0x0x0 = 0. Then, 0^0 = 1.
Even 0/0 = 1x0/1x0 = 1/1 = 1.
Today's arithmetic system seems to have two different systems in it: one to regard 0 simply as indefiniteness and another to regard 0 as 1x0 since 1 is the basis.
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So, zero seems to be closer to God than one.
Zero as a state of naught is different from zero as a number for arithmetic operation.
What we can understand easily is the zero as a number for arithmetic operation supported by one, the basis.
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Mar 2:19 And Jesus said unto them, Can the children of the bridechamber fast, while the bridegroom is with them? as long as they have the bridegroom with them, they cannot fast.