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holomorphic binary operators over naturals; generalized hyper operators
#10
I've been experimenting looking at these operators and I've become much more familiar with its structure. I can prove convergence now.

Let's suppose by contradiction that; for sufficiently large n:



However. It is clear that for some

1:

Therefore we write:



Now we know that

Therefore:



However this is a contradiction because for sufficiently large the left equation becomes much larger than the right. This is easy to deduce by the relation 1 above. Therefore to prove convergence we just need add the claim:






YES! We have convergence for all s.







An important theorem I have to prove is the following, I consider it a stern requirement of hyperoperators. For all and and




I'll mull over that for awhile.

also; hopefully:

for at least
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RE: holomorphic binary operators over naturals; generalized hyper operators - by JmsNxn - 08/03/2012, 06:43 PM

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