03/09/2021, 10:28 PM

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

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

for (the 2-ary version) we get

But then an example of computation proposed is

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

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

since they require summation and ratios to be defined.

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

and

But then an example of computation proposed is

Quote:3[0]2

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

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.