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hyper 0
Ok, at the beginning I was convinced that the grouping operation on fingers was just the arithmetic mean.

Quote:To start you would put a fingers in one hand and b fingers in the other. Next you would figure out how many groups of a fingers you had total. Then you would perform the sum (# of groups) + (# in each group ) which is the same as (# of groups) + a.

In that interpretation we have that given a sequence for , we can see this sequence as group of fingers where every group has fingers in it. So we define an "hyper 0" operator 

if  then  

for (the 2-ary version) we get


But then an example of computation proposed is
You have 5 fingers total.That is 1 and 2/3s groups of 3. So the answer is 5/3+3 = 14/3

So the groups are meant to be weighted and the operation is clearly not commutative anymore. In fact the operation proposed is the following. Let for . Define

if then  

for ,   and


It is clear that the solutions work in some way for preaddition. It is not clear to me how these two solutions can meet the requirment of fundamentality

Quote:3. This operation should be something that is fundamental

since they require summation and ratios to be defined.

MathStackExchange account:MphLee

Fundamental Law

Messages In This Thread
hyper 0 - by dantheman163 - 10/25/2009, 11:29 PM
RE: hyper 0 - by andydude - 10/26/2009, 01:43 AM
RE: hyper 0 - by MphLee - 03/09/2021, 10:28 PM

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