You are using "Match " Either items match or they don't 17and 18 don't
match, 17 1nd 17 are identical simply treats a float number which is as
close to an integer that the difference is meaningless. J also has
extended numbers if you want oodles of digits,The references mentioned
are quite clear.
a=. 16r32
a
1r2
Mathematically equivalent (agreed 16 apples in a box of 32 apples is
not the same as 1 apple in a box of 2)
Don
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
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