None required, the discussion was useful. Ak
On Mon., Jan. 9, 2023, 16:08 Don Kelly, <d...@shaw.ca> wrote: > My apology, Devon has pointed out that the operator can change the > tolerance from the default value. > > Don > > On 2023-01-06 11:00 p.m., Ak O wrote: > > Correct. Which is a property of the Operator. > > > > > > Ak > > > > On Fri., Jan. 6, 2023, 23:47 Devon McCormick, <devon...@gmail.com> > wrote: > > > >> They are the same under tolerance: > >> https://code.jsoftware.com/wiki/Help/Primer/Tolerance. > >> > >> On Sat, Jan 7, 2023 at 12:48 AM Ak O <akin...@gmail.com> wrote: > >> > >>> This is strictly based on the tolerance properties of the Operator not > >> the > >>> Type of the Operands (Iyiabo's Prime Theorem). > >>> > >>> > >>> (Integer) ,(Integer) NB. The question we are asking is, are > these > >>> Terms the same? > >>> (17) -: (17) > >>> 1 > >>> > >>> (Floating) ,(Integer) NB. So also we are asking, are these Terms > the > >>> same? > >>> (17.0)-:(17) > >>> 1 > >>> > >>> > >>> Ak > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> On Fri., Jan. 6, 2023, 20:29 Don Kelly, <d...@shaw.ca> wrote: > >>> > >>>> J has it right. > >>>> > >>>> (17+45+65+71+5) -: (17+45+65+71+5) is the match between two integer > >>>> sums-each of which gives the integer result as they have the same > >> boolean > >>>> representation and are equal-giving a "1" result > >>>> > >>>> (17.36+45.24+65.87+71.20+5.00) -: (17+45+65+71+5) is an attempt to > >>> compare > >>>> a floating point number with an integer-the result is floating point > >> and > >>> a > >>>> "0" result > >>>> > >>>> +/ 17.36 45.24 65.87 71.20 5.00 > >>>> > >>>> 204.67 > >>>> > >>>> (+/17+45+65+71+5) > >>>> > >>>> 203 > >>>> > >>>> > >>>> Don Kelly > >>>> > >>>> > >>>> > >>>> On 2023-01-05 4:06 a.m., Ak O wrote: > >>>>> These are both certainly Terms of Degree 2. > >>>>> They are not equalities. They are not the same Term. > >>>>> > >>>>> The point I mean to highlight is the represention (for the purpose of > >>>>> calculation). > >>>>> > >>>>> > >>>>> 16/32 is not 15/30 is not 8/16. An equivalence is 1/2. It should > >> never > >>> be > >>>>> mistaken for Expression Linear /Logarithmic. > >>>>> > >>>>> The problem is in cases where you apply an equivalence simplification > >>>>> improperly sequence wise. > >>>>> You loss coherence of the expression, (which often leads to settling > >> on > >>>> on > >>>>> approximation where resolution can be achieved). > >>>>> > >>>>> This is what we think we are saying. > >>>>> (17+45+65+71+5) -: (17+45+65+71+5) > >>>>> 1 > >>>>> This is what we are actually saying. > >>>>> (17.36+45.24+65.87+71.20+5.00) -: (17+45+65+71+5) > >>>>> 0 > >>>>> Or worse > >>>>> (17.99+45.99+65.99+71.99+5.99 ) -: (17+45+65+71+5) > >>>>> 0 > >>>>> > >>>>> In part, this is why the full representation should be favoured. > >>>>> > >>>>> Particularly for unknown cases where it is common to reach for > >>>> Infinities. > >>>>> I am rambling now. Let me know if this is not clear. > >>>>> > >>>>> > >>>>> Ak > >>>>> > >>>>> > >>>>> On Wed., Jan. 4, 2023, 22:18 Raul Miller,<rauldmil...@gmail.com> > >>> wrote: > >>>>>> On Wed, Jan 4, 2023 at 10:24 PM Ak O<akin...@gmail.com> wrote: > >>>>>>> File -> Wed Jan 4 03:40:07UTC 2023 > >>>>>>> The statement: > >>>>>>> So, there's no difference in Degree 1 2 1 0 0 0 and 1 2 1... > >>>>>>> > >>>>>>> This is not correct. These should not be seen as equalities. > >>>>>> That's an interesting perspective. > >>>>>> > >>>>>> It seems to me that both of these are polynomials of degree 2. If > >>>>>> they should have different degrees, what degrees should they have? > >> And > >>>>>> how would this be consistent with the opening sentence at > >>>>>> https://en.wikipedia.org/wiki/Degree_of_a_polynomial#: > >>>>>> > >>>>>> "In mathematics, the degree of a polynomial is the highest of the > >>>>>> degrees of the polynomial's monomials (individual terms) with > >> non-zero > >>>>>> coefficients." > >>>>>> > >>>>>> Thanks, > >>>>>> > >>>>>> -- > >>>>>> Raul > >>>>>> > >> ---------------------------------------------------------------------- > >>>>>> For information about J forums seehttp:// > >> www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >>>>> For information about J forums seehttp:// > >> www.jsoftware.com/forums.htm > >>>> ---------------------------------------------------------------------- > >>>> For information about J forums see > http://www.jsoftware.com/forums.htm > >>>> > >>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > >>> > >> > >> -- > >> > >> Devon McCormick, CFA > >> > >> Quantitative Consultant > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
