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Re: 0 = 1
Posted:
Oct 5, 2017 2:10 AM


Ross A. Finlayson explained on 10/5/2017 : > On Wednesday, October 4, 2017 at 7:59:00 PM UTC7, FromTheRafters wrote: >> Conway pretended : >>> On Wednesday, October 4, 2017 at 8:41:08 PM UTC5, FromTheRafters wrote: >>>> Ross A. Finlayson used his keyboard to write : >>>>> On Wednesday, October 4, 2017 at 12:42:13 PM UTC7, 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 socalled 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. >>> >>> >>> Ross >>> >>> I feel your post makes my point. I do not say this sarcastically or >>> rudely....as you say >>> >>> >>> "there MUST be ROOM for them all......" >>> >>> you however say...therefore this means numbers have NO space >>> >>> I however say... this means space and value are "interchangeable"...or >>> "relative" >>> >>> >>> "if it ain't broke don't fix it"...I agree >>> >>> but this does NOT mean >>> >>> "if it ain't broke don't improve upon it" >>> >>> there is always room for improvement >>> >>> as you say >>> >>> this all might seem pointless now...but later..... >> >> I'm not Ross, I was replying to Ross. I agree with Ross about you not >> being discouraged in your explorations just because of a lack of >> constructive criticism. > > This is Ross.
Hello Ross. This is who you replied to, and I have no such system being as I am comfortable with the systems we already have. Perhaps you meant to reply to Conway? He is the one with the duality of zero thing where zero's value can be chosen from amongst [1:0] to avoid a problem with denominators.
> I'd carry on with your alternating systems about numbers > then where you can define a notation to reflect the results, > about later having something like "equals" > having been overloaded or "0 not equals 1".
Choosing a numerical value of one for zero when it is in a denominator only makes more trouble IMO. A value infinitesimally short of infinity suddenly becomes one. If you started with 1/epsilon when epsilon is 'close' to zero (very big number) and gets switched to a one if the epsilon disappears (becomes actually zero) big discontinuity at the point of switching.
Better would be to take hints from the neighborhood around zero like the current standard system does with limits.
> So when you describe these value spaces and comment on > their properties it's pretty much always with a rather > limited, direct, expressive, and correct name and notation > in "mathematics" that it already has all its names just > from what it is.
Something is lost in translation here.
> That's not to say that anybody's paying attention, > even though they might and have constructive criticism > (or often and usually references to existing work). > > Anyways the structures have all their content then > for example 0 to 1 etcetera. > > It's how they do not that they don't, then for where > your definitions are sound when they fit with all your > other definitions.
Yeah, you completely lost me there.
Anyway, I'm sure Conway will read your post despite it being a reply to me.



