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Topic: Re: 0 = 1
Replies: 20   Last Post: Oct 5, 2017 3:03 PM

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Conway

Posts: 88
Registered: 9/21/17
Re: 0 = 1
Posted: Oct 5, 2017 3:05 AM
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On Thursday, October 5, 2017 at 1:10:42 AM UTC-5, FromTheRafters wrote:
> Ross A. Finlayson explained on 10/5/2017 :
> > On Wednesday, October 4, 2017 at 7:59:00 PM UTC-7, FromTheRafters wrote:
> >> Conway pretended :
> >>> On Wednesday, October 4, 2017 at 8:41:08 PM UTC-5, FromTheRafters wrote:
> >>>> 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.

> >>>
> >>>
> >>> 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






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