
Re: Is (t^29)/(t3) defined at t=3?
Posted:
Oct 10, 2013 7:02 AM


On Wednesday, October 9, 2013 4:49:09 AM UTC4, Peter Percival wrote: > Hetware wrote: > > > On 10/7/2013 8:39 PM, Peter Percival wrote: > > >> Hetware wrote: > > >>> On 10/7/2013 4:56 AM, David Bernier wrote: > > >>>> On 10/07/2013 03:21 AM, Robin Chapman wrote:
Heavy hitters on this thread, so where oh where is the discussion of the field requirements and their exception which is the source of the conflict? This goes back to operator theory, and the usage of division as fundamental does not hold up. This is because back in the field requirements, where division is laid out formally an exception was made for division by zero. Abstract algebra makes no treatment of division within its formal development of operator theory, and instead treats the arithmetic sum and product as fundamental.
We know that we are free to generalize the problem so that for any function g() we can build a function h which by algebraic principles is equal to g() but which will suffer the ambiguity at real a by setting h(x) = (( g(x) )( xa )) / ( x  a ) and it is the symbol '/' which should be scrutinized, for mathematics is not founded upon exceptional instances, and yet it can be exposed that the list of exceptions is not limited to zero. This is because there is a general dimensional math within which the quantity of exceptions rises in higher dimension. Though the two dimensional complex numbers still have only the zero exception the three dimensional form carries several more exceptional conditions, and these are positions whereby dimensional collapse is occurring. When we multiply by zero information is destroyed; the reverse operator does not hold any meaning. Within the three dimensional form the other exceptions include a reduction to one dimension and a reduction to two dimensions, as well as the reduction to zero dimensions in the old field requirement list. The list of exceptions continues to rise as we raise the working dimension.
This ambiguity is a valid attack upon existing mathematics. What will we do without the division operator? Division is still possible, but only when information is conserved. The information can be distorted and recovered, but when it drops a dimension (a discrete quality) then no reversal is possible. If this behavior carries physical correspondence then we must delve deeper into the system, and treat these fascinating qualities with more respect. It happens that these qualities yield arithmetic support for spacetime with unidirectional zero dimensional time.
Modern mathematics, as well as physics, treats the real number as fundamental, and this is a misnomer that has been purchased for some four hundred years. When it is exposed that the ray is more fundamental than the line; that the unidirectional ray is a finer representative of time; that the ray can go on to build the higher dimensional spaces with an arithmetic product; then the farce of modernity is upon us. Polysign numbers http://bandtechnology.com/PolySigned offer a new interpretation; more like a hammer and chisel than the swiss army knife of modern mathematics since they take us into high dimension immediately, and the hammer has power not offered before, exposing P1 as a fundamental sibling to the real number and their big sister; the complex number. The old real number folds into its swiss handle along with as many other contraptions as you care to carry around. Still, even under the polysign interpretation the physical meaning of the arithmetic product lacks physical correspondence, so what gives? There is much more work left to be done, but the context of modern mathematics is not reasonable to work from any more.
 Tim http://bandtechnology.com
> > >>>>> On 07/10/2013 04:34, Hetware wrote: > > >>>>>> On 9/30/2013 4:03 AM, Robin Chapman wrote: > > >>>>> > > >>>>>>> Hetware: 0/0 = 3 > > >>>>>>> > > >>>>>>> Ciekaw: 0/0 = 1 > > >>>>>>> > > >>>>>>> Any more entrants? > > >>>>>>> > > >>>>>> > > >>>>>> To be correct; Hetware: 0/0 = 1 (under certain circumstances). > > >>>>> > > >>>>> Not according to your original posting in this thread :( > > >>>> > > >>>> Heware, if 0/0 = 1, then 0/0 = (100*0)/0 = 100*(0/0) = 100*1 = 100. > > >>>> > > >>>> So, assuming 0/0 = 1, we find that 1 = 100 :( > > >>>> > > >>>> David > > >>>> > > >>> > > >>> That statement came with a qualification. That is, given a function > > >>> defined by f(t) = (t^29)/(t3), I could assume (t3)/(t3) = 1, even > > >>> where t=3. > > >> > > >> "given a function defined by" is irrelevant. At t=3 (t3)/(t3) is > > >> undefined. > > >> > > >>> I've already shown that a modified version of that > > >>> proposition does make sense. > > >> > > >> No you haven't. > > >> > > >>> Given a function f(t) continuous for all real numbers t and defined by > > >>> (t^29)/(t3) everywhere the expression is meaningful, that function is > > >>> identical to g(t) = (t+3). My original mistake was to assume continuity > > >>> after using (t^29)/(t3) to define the entire function. > > >> > > >> What you wish to say is that the function g:R>R defined by > > >> > > >> g(t) = f(t) if t=/=3 > > >> = 6 otherwise > > >> > > >> has these properties: > > >> i) g = f where f is defined, > > >> ii) g is defined on the whole of R, > > >> iii) g is continuous. > > >> > > >> > > >> > > > > > > The value of 6 at t=3 follows from the stipulation of continuity. > > > > The value of what? f or g? f has no value at 3. > > > > > It is > > > meaningful to say that f(t) is continuous over the domain of real > > > numbers. > > > > So what? Is it true? Yes, by proof, not by stipulation. > > > > > It is also meaningful to say that f(t) = (t^29)/(t3) > > > everywhere that the rhs is meaningful. > > > > I would say "f is defined everywhere (in R) that (t^29)/(t3) is defined". > > > > > That is sufficient information > > > to determine that f(3) = 6. > > > > f(3) doesn't equal anything. One may "fill the gap" by defining g as I > > have done above, *then* g(3) = 6. But g isn't f. > > > >  > > The world will little note, nor long remember what we say here > > Lincoln at Gettysburg

