A theroy for operators and functions

[alan2here]

http://img693.imageshack.us/img693/3950/calcw.png

 

http://rapidshare.com/files/325308950/operators.xlsx.html

http://www.filehosting.org/file/details/91934/operators.xlsx

 

Above is an image of a spreadsheet and two link to the spreadsheet itself.

 

My thoughts are based on the way that multiply can even if not the most efficient way of performing the calculation can be thought of as repeated add, and power repeated multiplication. Although there are differences beyond that and other calculations just as simple and multiply that don't have names.

 

Columns C and D of the spreadsheet show the descriptions of increment and decrement. Thease add and subtract 1. I don't show how thease occur as they are in my model the simplest components. In a way everything in the spreadsheet is describes as being some form of repeated increment and decrement.

 

Columns E and F show add and subtract. They take the inputs f and s meaning first and second.

 

f operator s = 6

2*3 = 6

 

The calculation for both starts at f and is incremented or decremented s times.

 

Unless what it means it is already evedent to you ignore the result row for now.

 

The next operation is multiply. This time we start at 0 not f and (add f) s times.

 

The next is devide. I should have put "untill >" in B7. This is a sort of bailout. You finish the calculation if this occurs. r means the result of the calculation and t means the number of times it occured before it was stoped. This is shown in column A.

 

Iv'e also filled in power but then got stuck on the next two. I'm also not sure if log takes f and s as parameters where f is the number and s is the base or if it is better to think of it as taking two parameters of equal importance as a function to take the averege of three numbers might. In this case it's inputs should perhaps be. s1 and s2 where 1 and 2 are subscript.

 

Can mod and log be neetly modeled in this way?

K2 as f, s or s1, s2?

What would go in L1?

Is there ever a time where both times and untill are populated?

Should I use differnt terminoligy anywere in my description?