Dividing by Zero, and the Orders of Infinity
This article got passed around this morning. I recommend ignoring the authors approach / intentions and focusing instead on the article until it leads up to the point he discusses infinity.
( read / skim the first part of that )
I think it’s rich that dividing by 0 ( as in x/0 ), in a single grade-school-math step, takes us right into the heart of the orders of infinity! I feel this can go an easy and powerful way to open the imagination to the realm of infinity. It may even so-easily allow some glimpse of the ‘mechanics’ of Zero, as a kind of infinity (nothing) that then divides other infinities.
This trick thinking in more detail on this may come from the secondary-abstraction of saying that x/0 equals some value r. x/0 = r As Zero is an infinity, the solution ( r ) becomes an infinity of the order x. This order could be any number, even another infinity – which I think takes us into the countable, uncountable and infinite Infinities. If x=7 then r is an infinity of a countable order. If x=(some form of infinity) then r is an infinity of the infinite-order x.
Intuitively, this feels like it sets the stage for a linking, or network, of the infinities.