02/21/2008, 07:22 PM

I think names should be given to these hyperoperations to make easier intuitive understanding.

As I understand it, positive zeration is counting, or enumeration, of infinite number of objects, while negative is counting of different objects (also infinite in number).

1 is infinite summation, or summation where order of terms does not matter as they are presumed to be infinite.

Halvation then is summation of any 2 enumerated , thirdation - any 3 etc. There is an imaginary part to these operations which corresponds to the number of ways these sums can be made from infinite numbers we have enumerated.

I would say there is a direct correspondance between imaginary part of 1/n ation and combinatorics.

The same applies to fractional operators between 1 and 2 - summation and multiplication.

They represent multiplication of finite number of objects. etc.

between 2-3 - exponentation of finite number of objects and related combinatorics expressed by?

between 3-4 - tetration of finite number of objects and related combinatorics expressed by?

I know I am not very clear about this, but for me it makes sense to establish a clear link between operations possible in mathematics and operations defined as hyperoperations-that would help intuitively to predict their properties- and by that clarify the operations used in mathematics in general.

Have You had any ideas about this?

Ivars

As I understand it, positive zeration is counting, or enumeration, of infinite number of objects, while negative is counting of different objects (also infinite in number).

1 is infinite summation, or summation where order of terms does not matter as they are presumed to be infinite.

Halvation then is summation of any 2 enumerated , thirdation - any 3 etc. There is an imaginary part to these operations which corresponds to the number of ways these sums can be made from infinite numbers we have enumerated.

I would say there is a direct correspondance between imaginary part of 1/n ation and combinatorics.

The same applies to fractional operators between 1 and 2 - summation and multiplication.

They represent multiplication of finite number of objects. etc.

between 2-3 - exponentation of finite number of objects and related combinatorics expressed by?

between 3-4 - tetration of finite number of objects and related combinatorics expressed by?

I know I am not very clear about this, but for me it makes sense to establish a clear link between operations possible in mathematics and operations defined as hyperoperations-that would help intuitively to predict their properties- and by that clarify the operations used in mathematics in general.

Have You had any ideas about this?

Ivars