GFR Wrote:Aim high! There is a lot of space !!!!

GFR

Ok, before Henryk catches me

Let us assume there is some right order in enumeration, kind of natural. Let us assume it goes from small to big (do not ask me what is small and big-perhaps numbers, so we enumerate numbers , e.g real numbers with natural ( I know its not possible, just as an example) ) . Then if we subtract in the "right " order, the small things from the big, so to say we do not destroy the order of enumeration we had used, we have still positive "numbers" as a result.

Now if we destroy the order of enumeration to exactly opposite, big to small, we have negative enumeration. When we change order in our positive enumeration we had and subtract big from small, we also end in negative teritory. So far this matches.

Now if we look what more we can do with perhaps more than 2 objects, we can reorder them in more then 2 ways - right and wrong, but also in a mixed ways so that outcome is not exactly opposite to right enumeration, but something mixed. Now perhaps (?) this mixed enumeration has to be somewhere in between rigth and wrong enumeration, perhaps it is fractional operation depending on the balance of the result.

Now there has to be an enumeration that makes it impossible to see have we mixed up things to the right or wrong direction, we can magnify the enumerated sequences, which may be infinite, as much as we want and still not able to decide is it right or wrong. That could be kind of "imagination".

If we apply this to a single number,base a, to be able to explain what such operation does - that requires some subtler structure to exist in a number which defines what will be result of "imagination" or "minusation"....

Ivars