Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Conway
Posts:
88
Registered:
9/21/17


Re: 0 = 1
Posted:
Oct 5, 2017 3:05 AM


On Thursday, October 5, 2017 at 1:10:42 AM UTC5, FromTheRafters wrote: > 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.
Rafters...
I apologize (again) for mis quoting you....
I have NEVER claimed that you can chose z1 or z2 in denominators
I claimed the exact opposite...in division
The numerator must be z1 the divisor must be z2



