Science Forums 2

[Turtle]

Originally Posted by Don Blazys

...
But, here is the real question:

If we have the multiplication:

,

then did we begin with and increase it by a factor of ,

or did we begin with and "increase" it by a factor of ?

You see, while it's clearly possible to increase unity by a factor of twenty-eight,
it's simply not possible to "increase" anything by a factor of unity,
so "multiplication by unity" can't possibly exist, and something that
can't possibly exist, can't possibly be defined!

Don.

Hi Don. Allow me some wordsmithing if you will here. Substitute your "increase" with "make arrangements of " and consider that you have actually piles of beans in the number that the numerals represent. In this case, the 1 * 28 has the expression " make 1 arrangement of 28" or "make 28 arrangements of 1", or vice versa if you write 28*1. The product is of course the sum of all arrangements then made.

I have mused over the apparent "error" in leaving out factors, including but not exclusive to 1. For example strictly following the rule for Perfect Numbers, i have argued that 1 is Perfect. Problem is, down the road it makes for all manner of inconsistencies as it makes 1 and not 6 the first Perfect. It's a fine philosophical debate, but there is good reason for settled conventions. A non-one example is the question of whether 16 is abundant or deficient, and it depends on if you count 4 twice as a factor. It is still not clear to me what repurcussions follow from counting it twice, but 16 is not alone in this as other squares also change their stripe on this condition.

With all the interest and discussion on your ideas, does anyone feel there is room to call it a "different algebra" and simply go about seeing what complications arise based on it?

That's a rap.