Not exactly. integer, integer --> possibly 17 -: 17 1 17-:18 0 floating,integer --> possibly 17.000000000000001-:17 1
18.000000000000001-:17 0 TermA,TermB --> The possibilities are 1 or 0 only, yes or no. It is not how. It is why. Whatever the basis is what it is. Ak On Sat., Jan. 7, 2023, 21:12 Don Kelly, <d...@shaw.ca> wrote: > integer, integer -- Yes >> >> >> > floating,integer, maybe.. > > In this case J converts the floating number to an integer(why not have a > computer language that doesn't require that a number must e defined as > integer vs floating point where the computer. can do it? Where it > matters, J provides ways to extend "precision" You reccognise that > "precision" is not necessarily exact. A value for pi is a useful > approximation ( but counting living people in your house should be exact. > > Significant figures, taught , at least back before the 1950's in > Physics,Mathematics, and Engineering (hammered home to me in 1950) . > > 17.00000001-:17 oops- 1 in > > 0 > > 17.000000000000001-:17 > > 1 > > - > > The tolerance limits in the above cases is not set by the operator but > by the number of bytes available in the machine memory.the display is > rounded off by the number of digits set by the operator. > > > Look at NuVoc Vocabulary/NumericPrecisions also > Vocabulary/AccurateSummation > > > > On 2023-01-06 9:48 p.m., Ak O 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 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
