Ross A. Finlayson used his keyboard to write : > On Wednesday, October 4, 2017 at 12:42:13 PM UTC-7, Conway wrote: >> Peter >> >> Correct me here if I'm wrong... >> >> This thread was over a week old with no replys... >> >> Why did you bring it back up if nothing had changed in your opinion? >> >> >> Only two scenarios exist... >> >> 1. Your just a troll >> 2. Something I said is nagging the back of your mind....saying...he may >> just be right. > > You might as well go on with your constructions > not receiving much shall we say constructive, > criticism. > > Though, you can readily expect others to understand > their constructive content.
I have not been fighting the idea, but it is my belief that he is trying to 'get around' some perceived problem with zero -- it being excluded from being a denominator. I feel that the so-called problem has already been solved via the Limit idea.
Ingrained in my mind is the idea that numbers are values devoid of any other thing such as he suggests like 'space'. The reason is by the surprising (to me at the time) idea that the rationals are not continuous. It would seem that due to the fact that denominators can be any natural number, perhaps infinitely large, that the 'distance' (or space?) between adjacent ones on the rational number line could be completely filled. Their being 'discreet' values had escaped me at the time.
Then there are irrational numbers arrived at by algebra (such as the squareroot of two) which must 'fit' between some two of these previously determined rational numbers. Okay, so that surely must fill the line up. These irrationals are algebraic and are countable. Then there are the transcendentals, and again there must be "room" for them. Uncountably many of them. I think that there must be no "width" to numbers at all on the real number line.
So bottom line:
1) If it ain't broke, don't fix it. 2) That doesn't mean such an idea is meaningless, in fact new math is often created while exploring things which for all intents and purposes *seem* meaningless to others at the time they are being explored. Euler's Totient function comes to mind here, I read somewhere that it was considered 'a neat trick, but what good is it' by other mathematicians of the time. It turns out to be quite useful today in simplifying calculations reducing the 'computing cost' of encryption related calculations.