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Yipogationaragazaiationalazed-zeroed is defined as 00.00000.000.03^^^^^^^^^432^(543x32^43). It is assumed to be smaller than 0, yet larger than any other Bloxin Hyper-Zero. The expression how is largely meaningless. See Calculation for details.




Calculation[]

The expression 00.00000.000.03^^^^^^^^^432^(543x32^43) is meaningless, first and foremost because 00.00000.000.03 has no clear meaning in decimal notation, but also because even if we interpret this as "0", 0 to an operation higher than exponentiation exhibits unusual behavior (we will examine that shortly). The top part of the expression however can easily be computed. 32^43 is approximately 5.26x10^64, and multiplying this by 543 is approximately 2.86x10^67 which we can also write as 10^67.46. Next we evaluate 432^10^67.46 which is 10^(10^67.46 * log(432)) ~ 10^10^67.88. This number lies between a suhtasillion and a googolplex.

Next we will begin with the assumption that 00.00000.000.03 = 0 and see what would happen. Firstly we can assume 0^N for large positive integer N = 0. What happens when we attempt to compute 0^^N? Well under one common interpretation 0^0 = 1. One can assert this in two ways. Firstly one can claim that anything to the 0th power is 1 by definition. However one justification for x^0 = 1, is because this expression is actually x/x. Since x in this case is 0, this could mean 0^0 = 0/0 which is indeterminate. We however can use calculus to define 0^0 as 1. We simply find the limit as x approaches 0 from the right of x^x. It turns out this specific limit is 1. If we accept this then we can say 0^^2 = 0^0 = 1. This leads to a strange sequence:

0^^1 = 0

0^^2 = 1

0^^3 = 0^0^^2 = 0^1 = 0

0^^4 = 0^0^^3 = 0^0 = 1

0^^5 = 0^0^^4 = 0^1 = 0

...

So tetrating 0 gives us an alternating sequence of 0,1,0,1,0,1,...etc. Note that 0^^0 following this pattern would be 1, and in fact 0^^N would be 1 if N is even and 0 if N is odd. If we then assume this is well defined we than have 0^^^2 = 0^^0 = 1. 0^^^3 = 0^^0^^0 = 0^^1 = 0, 0^^^4 = 0^^0^^^3 = 0^^0 = 1. etc. As can easily be gathered it also follows that 0^^^N would be 1 if N is even and 0 if N is odd. This would iterate through any number of up-arrows.

So the value of 0^^^^^^^^^N would depend on whether N was even or odd. Interestingly, because 432 is an even number, any positive integer power of it is also even. This can easily be seen since 432^N = 2^N * 216^N. and no matter the value of 216^N, 2^N will necessarily be an power of 2 and therefore an even number. This coincidently would suggest this value was 0.

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