Redefining RELATION
Putcha V. Narasimham
kenablersys@yahoo.com
What is a relation?
• Well known but difficult to define
• One ends up using association or connection
• They are just equ...
re·la·tion
• noun
• 1. an existing connection; a significant association
between or among things
• 2. connections in which...
Relation—Math definition
A relation is any subset
of a Cartesian product
 Consider two sets A & B
 Then, relation is a s...
Cartesian Product Definition
• Cartesian Product of two sets A & B
• Is a set of all ordered pairs <a,b>,
• Where
• ‘a’ is...
Cartesian Product Explanation
• Every member of A
• is paired with
• every member of B
• To generate CP
• CP is the full s...
Relation: A subset of Cartesian Product
22JUL13Need to Redefine RELATION
7
Relation
Set A
Men
Set B
Women
M1, M2, M3, M4,
...
Ordered Pairs OK, but is it a relation?
1. We only see WHO are related
2. But don’t know
 WHAT the relation is?
 WHAT br...
Is it a relation at all?
• It is just a set of ordered pairs
• WHAT is the basis to form pair?
• If any set is a relation,...
Ordered Pairs & Relations
• Related Ordered Pairs
• Father and daughter,
• Brother and sister
• Husband and wife
• Mixed p...
Arbitrary pairs remain unrelated
• One can form them but
what purpose do they
serve?
• What meaning or
significance do the...
Classes and Relations need basis
• This is the
motivation for
this proposal
22JUL13Need to Redefine RELATION
12
 Classes ...
Relation is as fundamental as set
 Is a member of is a relation
between an object and the set to
which it belongs
 The c...
Relation Redefined for clarity and use
• The mathematical definition of relation
appears unmathematical and leaves many
qu...
Proposed Definition of relation
A relation between two sets A and
B is a named set of principles and
criteria, according t...
How does this definition help?
• Now, we know what a relation is and how to
use it without forming ordered pairs first
• W...
Let’s THINK and Discuss
• A definition should be clear, consistent
and self-sufficient for application and
use.
• I believ...
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Relation--Need for Radical Redefinition PPT

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Relation.....too fundamental to be ill-defined but is it well defined? Is it useful? Not quite according to me. I have my questions and reasons to redefine relation radically. Here is the proposal.

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Relation--Need for Radical Redefinition PPT

  1. 1. Redefining RELATION Putcha V. Narasimham kenablersys@yahoo.com
  2. 2. What is a relation? • Well known but difficult to define • One ends up using association or connection • They are just equivalent to relation • But NOT definitions! • Let’s look up online dictionary • http://dictionary.reference.com/browse/relation?s=t 22JUL13Need to Redefine RELATION 2 Relation What is it?
  3. 3. re·la·tion • noun • 1. an existing connection; a significant association between or among things • 2. connections in which persons or things are brought together • Well these are NOT precise and rigorous enough • But one can get an idea of what a relation is • Let’s see Math definition 22JUL13Need to Redefine RELATION 3 How is rain related to clouds?
  4. 4. Relation—Math definition A relation is any subset of a Cartesian product  Consider two sets A & B  Then, relation is a subset of CP of A&B 22JUL13Need to Redefine RELATION 4 Relation: Subset of CP of A & B Set A Men Set B Women
  5. 5. Cartesian Product Definition • Cartesian Product of two sets A & B • Is a set of all ordered pairs <a,b>, • Where • ‘a’ is an element of A & • ‘b’ is an element of B 22JUL13Need to Redefine RELATION 5 Set A Men Set B Women
  6. 6. Cartesian Product Explanation • Every member of A • is paired with • every member of B • To generate CP • CP is the full set of all possible pxq ordered pairs 22JUL13Need to Redefine RELATION 6 Set A Men Set B Women M1 Mp W1 W2 Wq
  7. 7. Relation: A subset of Cartesian Product 22JUL13Need to Redefine RELATION 7 Relation Set A Men Set B Women M1, M2, M3, M4, M5, M6, M7 … M20 W1, W2, W3, W4, W5, W6, W7… W30 Subset M2, W4 M4, W7 M5, W10 M9, W1 M13, W27
  8. 8. Ordered Pairs OK, but is it a relation? 1. We only see WHO are related 2. But don’t know  WHAT the relation is?  WHAT brings them into a relation?  And, HOW are they related? 22JUL13Need to Redefine RELATION 8 Subset M2, W4 M4, W7 M5, W10 M9, W1 M13, W27
  9. 9. Is it a relation at all? • It is just a set of ordered pairs • WHAT is the basis to form pair? • If any set is a relation, how is one relation different from another, except for the exact pairs? • Is it not possible that the same pairs are also related differently? 22JUL13Need to Redefine RELATION 9 Subset M2, W4 M4, W7 M5, W10 M9, W1 M13, W27
  10. 10. Ordered Pairs & Relations • Related Ordered Pairs • Father and daughter, • Brother and sister • Husband and wife • Mixed pairs for games • Pairing alone is not relation • Basis for pairing is relation 22JUL13Need to Redefine RELATION 10 Relation is the basis for pairing NOT just pairs
  11. 11. Arbitrary pairs remain unrelated • One can form them but what purpose do they serve? • What meaning or significance do they have? • In businesses, societies and nature there are always principles and criteria guiding the formation of classes (categories) and relations • They are important 22JUL13Need to Redefine RELATION 11
  12. 12. Classes and Relations need basis • This is the motivation for this proposal 22JUL13Need to Redefine RELATION 12  Classes and relations need a set of principles and criteria for the their formation as in OOAD, UML  They have identities and properties for use and application
  13. 13. Relation is as fundamental as set  Is a member of is a relation between an object and the set to which it belongs  The concept of relation and set perhaps emerge interdependently and simultaneously This may have been sorted out in some fundamental theories of mathematics and or philosophy 13 22JUL13Need to Redefine RELATION
  14. 14. Relation Redefined for clarity and use • The mathematical definition of relation appears unmathematical and leaves many questions unanswered • It is enumerative & unusable • Runs into anomalies and paradoxes • So, here is a proposed definition of relation 22JUL13Need to Redefine RELATION 14
  15. 15. Proposed Definition of relation 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.  Criteria for forming ordered pairs are more important than the pairs  This resolves many questions  See PDF--Relation: Need for Radical Redefinition 15 22JUL13Need to Redefine RELATION
  16. 16. How does this definition help? • Now, we know what a relation is and how to use it without forming ordered pairs first • We know how relation applies for the FUTURE members of sets involved • We can use it to define, create, VERIFY and apply relations correctly and infer from them 22JUL13Need to Redefine RELATION 16
  17. 17. Let’s THINK and Discuss • A definition should be clear, consistent and self-sufficient for application and use. • I believe the proposed definition is • I welcome reviews, examples, counter examples and feedback 22JUL13Need to Redefine RELATION 17 START kenablersys@yahoo.com

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