Relation --Need for Radical Redefinition PDF

Putcha V. Narasimham
Knowledge Enabler Systems Founder Professor & Proprietor
Temporary Address: 1924, Hamilton Avenue, Belmon CA
kenablersys@yahoo.com or putchavn@yahoo.com
Relation---Need for Radical Redefinition Page No 1 of 6
The Best Anywhere Must Reach the Needy Everywhere
Relation:NeedforRadicalRedefinition
Our Ref: Footer
Date: 25JUL13
I'm not smarter than anyone else,
I just think about things more
Albert Einstein
Being competent, effective and efficient is
90% mindset and 10% toolset.
---Roger Tregear
Let’s start with
A relation is any subset of a Cartesian product.
For instance, a subset of A x B called a "binary relation from
A to B is a collection of ordered pairs (a,b) with first
components from A and second components from B.
http://mathworld.wolfram.com/Relation.html
1. OBSERVATION
When I applied this definition of
"Relation" (to Entity Relationship
Diagram and Associations in Object
Oriented Analysis and Design), I found
that there is “No Principle or Criterion"
based on which ordered pairs may be

formed to represent WHAT are
RELATED & HOW. There is no
significance for the name of relation nor
its meaning.
2. THE PROBLEM
There seems to be a serious flaw. The
definition simply enumerates the
ordered pairs from two sets and calls it
a relation. It lists which members of the
two sets are related but fails to state
what brings them into a relation and
what the relation is. There is NO
indication of WHY or HOW a relation
may arise and how many kinds of
relations may exist. This causes a
problem in ascertaining if a "relation" is
properly applied. This way, we only
know who or which are related but NOT
know what the relation is. A serious
problem.
3. EXAMPLE
Let's consider A, a set of men and B, a
set of women and see the problems.
3A: If a relation "is husband of" is to be
defined from A to B, one has to state the
principle based on which a member of B
is to be selected for a member of A.
3B: Similarly if a relation "is brother of" is to
be defined from A to B, one has to state
another principle based on which a

member of B is to be selected for a
member of A.
4. NO BAISIS
Not stating the criterion (or principle) of
associating removes the basis of
forming a set of ordered pairs.
4A: Consequently, what the “relation is” is
not known till some sub-set of Cartesian
Product between two sets is created but
why or how any such subset may be
formed is not known and so no valid
subset can be formed.
4B: Some random subsets may be formed
and any random subset would be a
“relation” without any known properties
since their formation itself is baseless or
random. Of course, one may consider
randomness itself to be a property and
that may serve some purpose. Let it be.
5: HIDDEN CRITERIA
It appears that some unstated but
useful criteria are indeed applied in
practice to form and verify relations,
correcting the serious flaw in the
definition but leaving the definition as
such.
5A: In the example given in point 3, there is
no basis to form or verify the relation “Is
husband of” or “Is brother of” according

to the definition of relation but relation
itself would be meaningless.
5B: Even when the ordered pairs are formed
according to some criteria, there is no
way to name the relation to refer to
those criteria and carry the criteria as a
part of relation. So, many factors are
missing.
6: THE PRAPOSAL
So, I find there is a need for Radical
Redefinition of Relation for informed
use / applications. Here is my proposal:
6A: Without knowing the principle of
relation, no ordered pairs can be formed
and called a relation. No relation can
arise and abide (hold) between two sets
whose members are arbitrarily paired
even though ordered. A set of ordered
pairs, not satisfying specified criteria of
relation, is just a set of ordered pairs but
NOT relation.
6B: From the sets A and B, if a new set of
ordered pairs can be formed according
to some criteria heretofore not known,
the investigator cannot claim to have
found a relation merely by enumerating
the pairs. The investigator has to
“necessarily fit a hypothesis to the
observation and define the principle of

the relation and give a unique name to
such relation”.
6C: Proposed definition: A relation
between two sets A and B is a named
set of principles and criteria, according
to which ordered pairs can be formed
from A and B
This is a binary relation but it can be
extended to reflexive and n-ary relations.
All other properties and conditions of
set theory hold.
6D: Some Properties of Relation:
 Those who are related through any
relation will be a subset of the
Cartesian product of sets A and B.
 The principles and criteria must be
applicable to the sets involved.
 For certain relations, ordered pairs
may or may not exist.
 The number of possible relations
between any two sets may vary from
Zero to many.
 Two or more relations having the
same ordered pairs are equivalent, if
and only if the named set of
principles and criteria to form them
are also the same.

Pain of unresolved issues
For long I lived in pain with what I found to be
a flaw. I sought clarifications from many
sources of knowledge---perhaps not the right
ones. Unfortunately, none of them gave any
convincing reasons for or against the original
definition or the flaw pointed out or the
proposed definition. That has been even
more painful.
I could be wrong
It is possible that my thinking and
understanding are flawed. I need to know
what’s wrong and what the resolution is.
LinkedIn and SlideShare provide excellent
opportunities to discuss topics though all of
them do not lead to agreement or resolution.
Thinking & discussions help
I have no claim to smartness. In fact, I have
serious disappointment at not being smart
enough. Yet, I believe thinking and discussion
help. Comments with reasons and citation
are most welcome.
Thanks and regards,
Cordially,

Relation --Need for Radical Redefinition PDF

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