"You do not show how to access particular rows or columns or elements from a
table".
The table, and the table name, is addressed by 00.
The left column, and the left column header, is addressed by 01.
The right column, and the right column header, is addressed by 02.
The upper row, and the upper row header, is addressed by 10.
The upper left table entry, and its data content, is addressed by 11.
The upper right table entry, and its data content, is addressed by 12.
The lower row, and the lower row header, is addressed by 20.
The lower left table entry, and its data content, is addressed by 21.
The lower right table entry, and its data content, is addressed by 22.
"without knowing the number of rows or columns."
In the example there are two rows and two columns.
If you need a third row, call it 30.
"Why not the concept of arrays with an index?"
Arrays may have different shapes. Any ordinal fraction has the shape (_$9).
Arrays have elements. Ordinal fractions don't.
Only array elements contains data. Any ordinal fraction may contain data.
Arrays may have subarrays. Any ordinal fraction has subordinate ordinal
fractions.
Arrays and atoms have names. Ordinal fractions don't.
"the set of Natural numbers begin with 1 yet we use base 10 representation that
uses 0."
Cardinal numbers and ordinal fractions have similarities and differences.
Cardinal number 0 (meaning "nothing") is not the same thing as ordinal fraction
0 (meaning "everything").
Cardinal number 1 (meaning "one") is not the same thing as ordinal fraction 1
(meaning "first part").
Using "0" for wild card character does not get along with using "0" for
counting to ten.
A cardinal number is represented by a right-justified sequence of digits with a
finite number of nonzero digits. The cardinal number 1 may be written 00001.
An ordinal fraction is represented by a left-justified sequence of digits with
a finite number of nonzero digits. The ordinal fraction 1 may be written 10000.
"However this was not an easy system in which to do arithmetic so I cannot see
how your base 9 system could be either."
Cardinal numbers, A and B, are ordered such that either A=B or A<B or A>B. For
example: 0=0 and 0<1 and 1>0 (meaning "zero is equal to zero" , and "zero is
fewer than one", and "one is more than zero").
Ordinal fractions, A and B, are ordered such that either A=B or A<B or A>B or
A<>B or A><B. For example: 0=0 and 0>1 and 1<0 and 10<>01 and 1><2. (meaning
that the whole is equal to the whole, and the whole comprises the first part,
and the first part is part of the whole, and the first half is compatible with
the odd fourths, and the first part is disjoint with the second part).
The notation for ordinal fractions makes ordinal fraction arithmetic easy, just
as the notation for cardinal numbers makes cardinal number arithmetic easy.
Keep asking!
Bo.
Den 18:35 torsdag den 7. juni 2018 skrev Donna Y <dy...@sympatico.ca>:
UDC is a library classification system akin to the Dewey decimal system—the
creators collaborated with Dewy. UTC is also used for data.
> Every number is thought of as a decimal fraction with the initial decimal
> point omitted, which determines the filing order.
I am not sure why you say it cannot handle tables.
> Concepts are organized in two kinds of tables in UDC:[27]
> <https://en.wikipedia.org/wiki/Universal_Decimal_Classification#cite_note-UDC_Structure-27>
> Common auxiliary tables (including certain auxiliary signs). These tables
> contain facets of concepts representing, general recurrent characteristics,
> applicable over a range of subjects throughout the main tables, including
> notions such as place, language of the text and physical form of the
> document, which may occur in almost any subject. UDC numbers from these
> tables, called common auxiliaries are simply added at the end of the number
> for the subject taken from the main tables. There are over 15,000 of common
> auxiliaries in UDC.
> The main tables or main schedules containing the various disciplines and
> branches of knowledge, arranged in 9 main classes, numbered from 0 to 9 (with
> class 4 being vacant). At the beginning of each class there are also series
> of special auxiliaries, which express aspects that are recurrent within this
> specific class. Main tables in UDC contain more than 60,000 subdivisions.
Can you show exactly what is gained by your “ordinal fraction”?
Also—the set of Natural numbers begin with 1 yet we use base 10 representation
that uses 0.
However in the 4 BCE the Greeks used their letters to represent numbers from
one to nine with no zero:
alpha beta gamma delta epsilon digamma zeta eta theta
They didn’t need to use 0 for higher values because much like Romans they had
symbols for higher values.
However this was not an easy system in which to do arithmetic so I cannot see
how your base 9 system could be either.
You suddenly use 0 when you illustrate tables. You do not show how to access
particular rows or columns or elements from a table but instead use vague
terms upper, lower, left, right without knowing the number of rows or columns..
Why not the concept of arrays with an index?.
Maybe you could explain what I am missing.
Donna Y
dy...@sympatico.ca
> On Jun 7, 2018, at 3:47 AM, 'Bo Jacoby' via Chat <c...@jsoftware.com> wrote:
>
> Ordinal Fractions is an improvement to the idea behind the Universal Decimal
> Classification (UDC).
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