File location naming hierarchy

• US 20060015538A1
• Filed: 12/06/2004
• Published: 01/19/2006
• Est. Priority Date: 06/30/2004
• Status: Active Grant

• Current Assignee: Lower48 IP, LLC (Lower48 Analytics, Inc.), Virginia T. Jenkins
• Original Assignee: Robert T. and Virginia T. Jenkins as Trustees for the Jenkins Family Trust Dated February 8, 2002
• Inventors: LeTourneau, Jack J.
• Granted Patent: US 7,882,147 B2
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G06F 16/10 File systems; File servers

Abstract

Embodiments of methods, apparatuses, devices and/or systems for a file location naming hierarchy are disclosed.

Claims

1. An article comprising:

a storage medium;

said storage medium having stored thereon a file location naming hierarchy;

wherein said hierarchy comprises at least a multi-set (MS) of a set of elements.

2. The article of claim 1, wherein said MS of a set of elements comprises a MS of a MS of said set of elements.

3. The article of claim 1, wherein said set of elements comprise natural numerals.

4. The article of claim 1, wherein said hierarchy further comprises compound multi-sets of said set of elements.

112. The apparatus of claim 111, wherein said computing platform is further adapted to form another finite multi-set from another numeral pair;

wherein manipulating said finite multi-set comprises combining said finite multi-sets.

113. The apparatus of claim 112, wherein said computing platform is further adapted to combine said finite multi-sets by multiplying the associated natural numerals.

114. The apparatus of claim 112, wherein said computing platform is further adapted to combine said finite multi-sets by merging the associated numeral pairs.

5. A method comprising:

forming a file location naming hierarchy;

wherein said hierarchy comprises at least a multi-set (MS) of a set of elements.

6. The method of claim 5, wherein said MS of a set of elements comprises a MS of a MS of said set of elements.

7. The method of claim 5, wherein said set of elements comprise natural numerals.

8. The method of claim 5, wherein said hierarchy further comprises compound multi-sets of said set of elements.

9. A method of arranging files in a file location naming hierarchy comprising:

forming a multi-set from a set of elements;

forming at least one more multi-set from said multi-set;

wherein said hierarchy comprises the multi-sets.

10. The method of claim 9, wherein said forming at least one more multi-set comprises recursively forming at least one compound multi-set.

11. The method of claim 10, wherein said recursively forming at least one compound multi-set comprises recursively forming a plurality of compound multi-sets.

12. An article comprising:

a storage medium having stored thereon instructions that, when executed, result in execution of a method of arranging files in a file location naming hierarchy as follows;

forming a multi-set from a set of elements;

forming at least one more multi-set from said multi-set;

wherein said hierarchy comprises the multi-sets.

13. The article of claim 13, wherein said instructions when executed further result in:

said forming at least one more multi-set comprising recursively forming at least one compound multi-set.

14. The article of claim 13, wherein said instructions, when executed, further result in:

said recursively forming at least one compound multi-set comprising recursively forming a plurality of compound multi-sets.

15. A method of associating a natural numeral with a multi-set comprising:

for the numeral 2, assigning a unique multi-set; and

for even composite numerals 2K, assigning the merger of the multi-set for 2 with the multi-set for K.

16. The method of claim 15, and further comprising:

for the numerals 0 and 1, assigning additional unique multi-sets; and

for odd non-composite numerals, assigning the associated Kleene enumeration index.

17. The method of claim 16, and further comprising:

for composite numerals K*L, assigning the merger of the multi-set for K with the multi-set for L.

18. The method of claim 16, wherein, for the numerals 0 and 1, assigning additional unique multi-sets comprises assigning the empty set and singleton zero, respectively.

19. The method of claim 15, wherein, for the numeral 2, assigning a unique multi-set comprises assigning doubleton zero.

20. An article comprising:

a storage medium having stored thereon instructions that, when executed, result in a method of associating a natural numeral with a multi-set as follows;

for the numeral 2, assigning a unique multi-set; and

for even composite numerals 2K, assigning the merger of the multi-set for 2 with the multi-set for K.

21. The article of claim 20, wherein said instructions, when executed, further result in:

for the numerals 0 and 1, assigning additional unique multi-sets; and

for odd non-composite numerals, assigning the associated Kleene enumeration index.

22. The article of claim 21, wherein said instructions, when executed, further result in:

for composite numerals, K*L, assigning the merger of the multi-set for K with the multi-set for L.

23. The article of claim 21, wherein said instructions, when executed, further result in:

for the numerals 0 and 1, assigning additional unique multi-sets comprising assigning the empty set and singleton zero, respectively.

24. The article of claim 20, wherein said instructions, when executed, further result in:

for the numeral 2, assigning a unique multi-set comprising assigning doubleton zero.

25. A method of associating a natural numeral with a numeral pair comprising:

forming said numeral pair so that it includes a Kleene enumeration index natural numeral corresponding to a non-composite numeral and another numeral that produces said natural numeral when multiplied with said non-composite numeral.

26. The method of claim 25, wherein said natural numeral that comprises a non-composite numeral is designated by said another numeral of said numeral pair comprising the numeral 1.

27. The method of claim 25, and further comprising:

forming a finite multi-set from said numeral pair.

28. The method of claim 27, and further comprising:

manipulating said finite multi-set.

29. The method of claim 28, and further comprising:

forming another finite multi-set from another numeral pair;

wherein said manipulating said finite multi-set comprises;

combining the finite multi-sets.

30. The method of claim 29, wherein said combining the finite multi-sets comprises:

multiplying the associated natural numerals.

31. The method of claim 29, wherein said combining the finite multi-sets comprises:

merging the associated numeral pairs.

32. The method of claim 25, and further comprising:

associating another natural numeral with another numeral pair; and

multiplying the natural numerals by merging the associated numeral pairs.

33. The method of claim 32, wherein said merging numeral pairs comprises:

combining [a,b] with [c,d] as follows;

[a, b*Q(c)″

*d], in which “

*”

represents multiplication and where the function Q(c) is a function that provides the non-composite numeral associated with the index c, as for the Kleene enumeration.

34. The method of claim 32, wherein said numeral pairs are represented as binary numerals, and said multiplying said natural numerals includes using the same or fewer bits than associated with binary representations of said natural numerals by merging the binary numeral pairs.

35. The method of claim 25, wherein said natural numeral is represented by a binary numeral representation of said numeral pair.

36. An article comprising:

a storage medium having stored thereon instructions that, when executed, result in execution of a method of associating a natural numeral with a numeral pair as follows;

forming said numeral pair so that it includes a Kleene enumeration index natural numeral corresponding to a non-composite numeral and another numeral that produces said natural numeral when multiplied with said non-composite numeral.

37. The article of claim 36, wherein said instructions, when executed, further result in:

said natural numeral that comprises a non-composite numeral being designated by said another numeral of said numeral pair comprising a numeral 1.

38. The article of claim 36, wherein said instructions, when executed, further result in:

forming a finite multi-set from said numeral pair.

39. The article of claim 38, wherein said instructions, when executed, further result in:

manipulating said finite multi-set.

40. The article of claim 39, wherein said instructions, when executed, further result in:

forming another finite multi-set from another numeral pair;

wherein manipulating said finite multi-set comprises;

combining the finite multi-sets.

41. The article of claim 40, wherein said instructions, when executed, further result in:

said combining the finite multi-sets comprising multiplying the associated natural numerals.

42. The article of claim 40, wherein said instructions, when executed, further result in:

said combining the finite multi-sets comprising merging the associated numeral pairs.

43. The article of claim 36, wherein said instructions, when executed, further result in:

associating another natural numeral with another numeral pair; and

multiplying the natural numerals by merging the associated numeral pairs.

44. The article of claim 43, wherein said instructions, when executed, further result in:

said merging the associated numeral pairs comprising combining [a,b] with [c,d] as follows;

[a, b*Q(c)″

*d], in which “

*”

represents multiplication and where the function Q(c) is a function that provides the non-composite numeral associated with the index c, as for the Kleene enumeration.

45. The article of claim 43, wherein said instructions, when executed, further result in:

said numeral pairs being represented as binary numerals; and

said multiplying said natural numerals including using the same or fewer bits than associated with binary representations of said natural numerals by merging the binary numeral pairs.

46. The article of claim 36, wherein said instructions, when executed, further result in:

said natural numeral being represented by a binary numeral representation of said numeral pair.

47. An article comprising:

a storage medium having stored thereon a table;

wherein said table uniquely associates a plurality of natural numerals with a plurality of numeral pairs, wherein at least one of the numerals for each of said pairs represents an index for the Kleene enumeration.

48. The article of claim 47, wherein said table further uniquely associates a plurality of finite multi-sets with said natural numerals and said numeral pairs.

49. The article of claim 48, wherein, for the numerals 0, 1, and 2, the associated multi-sets comprise the empty set, singleton zero and doubleton zero, respectively.

50. The article of claim 49, wherein, for composite numerals 2K, the associated multi-set comprises a merger of singleton zero with the multi-set associated with K.

51. The article of claim 50, wherein, for composite numerals K*L, the associated multi-set comprises a merger of the multi-set associated with K with the multi-set associated with L.

52. A method comprising:

uniquely associating a plurality of natural numerals with a plurality of numeral pairs, wherein at least one of the numerals for each of said pairs represents an index for the Kleene enumeration.

53. The method of claim 52, wherein uniquely associating further comprises uniquely associating a plurality of finite multi-sets with said natural numerals and said numeral pairs.

54. The method of claim 53, wherein uniquely associating, for the numerals 0, 1, and 2, comprises associating the multi-sets empty set, singleton zero and doubleton zero, respectively.

55. The method of claim 54, wherein uniquely associating, for composite numerals 2K, comprises associating the multi-set comprising a merger of singleton zero with the multi-set associated with K.

56. The method of claim 55, wherein uniquely associating, for composite numerals K*L, comprises associating the multi-set comprising a merger of the multi-set associated with K with the multi-set associated with L.

57. A method of forming a binary tree file location naming hierarchy from a finite multi-set comprising:

associating said finite multi-set with a natural numeral; and

associating a first non-composite numeral and a second non-composite numeral with said natural numeral, said non-composite numerals and said finite multi-set forming at least a portion of said hierarchy.

58. The method of claim 57, wherein said finite multi-set represents a named location for a file in said hierarchy, and said first and second non-composite numerals represent additional named locations for related files in said hierarchy.

59. The method of claim 57, and further comprising associating a plurality of binary trees with finite multi-sets, each binary tree associated with a finite multi-set further associated with two or more natural numerals larger than one.

60. An article comprising:

a storage medium having stored thereon instructions that, when executed, result in;

a method of forming a binary tree file location naming hierarchy from a finite multi-set as follows;

associating said finite multi-set with a natural numeral; and

associating a first non-composite numeral and a second non-composite numeral with said natural numeral, said non-composite numerals and said finite multi-set forming at least a portion of said hierarchy.

61. The article of claim 60, wherein said instructions, when executed, further result in:

said finite multi-set representing a named location for a file in said hierarchy, and said first and second non-composite numerals representing additional named locations for related files in said hierarchy.

62. The article of claim 60, wherein said instructions, when executed, further result in:

associating a plurality of binary trees with finite multi-sets, each binary tree associated with a finite multi-set further associated with two or more natural numerals larger than one.

63. A method comprising:

associating at least some files of a file location naming hierarchy with non-composite numerals.

64. The method of claim 63, wherein said associating comprises associating said at least some files in said file location naming hierarchy with non-composite numerals and/or products of non-composite numerals;

and further comprising;

moving between said at least some files including dividing and/or multiplying said non-composite numerals and/or associated products with non-composite numerals.

65. The method of claim 64 wherein said associating comprises associating other files other than said at least some files with non-composite numerals.

66. The method of claim 65, wherein said moving between said at least some files comprising dividing and/or multiplying with non-composite numerals.

67. The method of claim 64, wherein said associating comprises associating said at least some files with non-composite numerals;

and

said moving between said at least some files comprising multiplying and/or dividing by a non-composite numeral.

68. An article comprising:

a storage medium having stored thereon instructions that, when executed results in execution of a method as follows;

associating at least some files of a file location naming hierarchy with non-composite numerals.

69. The article of claim 68, wherein said instructions when executed further result in:

said associating comprising associating said at least some files in said file location naming hierarchy with non-composite numerals and/or products of non-composite numerals; and

further result in;

moving between said at least some files including dividing and/or multiplying said non-composite numerals and/or associated products with non-composite numerals.

70. The article of claim 69, wherein said instructions when executed further result in:

said associating comprising associating other files other than said at least some files with non-composite numerals.

71. The article of claim 70, wherein said instructions when executed further result in:

said moving between said at least some files comprising dividing and/or multiplying with non-composite numerals.

72. The article of claim 69, wherein said instructions when executed further result in:

said associating comprising associating said at least some files with non-composite numerals; and

said moving between said at least some files comprising multiplying and/or dividing by a non-composite numeral.

73. An apparatus comprising:

a computing platform;

said computing platform having stored thereon a file location naming hierarchy;

wherein said hierarchy comprises at least a multi-set (MS) of a set of elements.

74. The apparatus of claim 73, wherein said MS of a set of elements comprises a MS of a MS of said set of elements.

75. The apparatus of claim 73, wherein said set of elements comprise natural numerals.

76. The apparatus of claim 73, wherein said hierarchy further comprises compound multi-sets of said set of elements.

77. An article comprising:

a file having a named file location;

said named location having been formed at least by;

forming a file location naming hierarchy;

wherein said hierarchy comprises at least a multi-set (MS) of a set of elements.

78. The article of claim 77, wherein said file having a named location having further been formed at least by:

said MS of a set of elements comprising a MS of a MS of said set of elements.

79. The article of claim 77, wherein said file having a named location having further been formed at least by:

said set of elements comprising natural numerals.

80. The article of claim 77, wherein said file having a named location having further been formed at least by:

said hierarchy comprising compound multi-sets of said set of elements.

81. An article comprising:

a file having a named location having been arranged in a file location naming hierarchy having been formed at least by;

forming a multi-set from a set of elements;

forming at least one more multi-set from said multi-set;

said hierarchy comprising the multi-sets.

82. The article of claim 81, wherein said named location having further been formed at least by forming at least one more multi-set comprising recursively forming at least one compound multi-set.

83. The article of claim 82, wherein said named location having further been formed at least by said recursively forming at least one compound comprising recursively forming a plurality of compound multi-sets.

84. An apparatus comprising:

a computing platform;

said computing platform adapted to form a multi-set from a set of elements;

adapted to form at least one more multi-set from said multi-set; and

adapted so that said hierarchy comprises the multi-sets.

85. The apparatus of claim 84, wherein said computing platform is adapted to form at least one more multi-set by recursively forming at least one compound multi-set.

86. The apparatus of claim 85, wherein said computing platform is adapted to recursively forming at least one compound multi-set by recursively forming a plurality of compound multi-sets.

87. An article comprising:

a file having a named location;

said named location being formed from a multi-set associated with a natural numeral at least by;

for 2, assigning a unique multi-set; and

for even composite numerals, 2K, assigning the merger of the multi-set for 2 with the multi-set for K.

88. The article of claim 87, said named location being formed from a multi-set further associated with a natural numeral at least by:

for 0 and 1, assigning additional unique multi-sets; and

for odd non-composite numerals, assigning the associated Kleene enumeration index.

89. The article of claim 88, said named location being formed from a multi-set further associated with a natural numeral at least by:

for composite numerals, K×

L, assigning the merger of the multi-set for K with the multi-set for L.

90. The article of claim 88, said named location being formed from a multi-set further associated with a natural numeral at least by:

for 0 and 1, assigning unique multi-sets comprises assigning the empty and singleton zero, respectively.

91. The article of claim 87, said named location being formed from a multi-set further associated with a natural numeral at least by:

for 2, assigning a unique multi-set comprises assigning doubleton zero.

92. An apparatus comprising:

a computing platform;

said computing platform being adapted to associate a natural numeral with a multi-set as follows;

for 2, assigning a unique multi-set; and

for even composite numerals, 2K, assigning the merger of the multi-set for 2 with the multi-set for K.

93. The apparatus of claim 92, wherein said computing platform is further adapted to:

for 0 and 1, assign additional unique multi-sets; and

for odd non-composite numerals, assign the associated Kleene enumeration index.

94. The apparatus of claim 93, wherein said computing platform is further adapted to:

for composite numerals, K×

L, assign the merger of the multi-set for K with the multi-set for L.

95. The apparatus of claim 93, wherein said computing platform is further adapted to:

for 0 and 1, assign unique multi-sets comprising the empty set and singleton zero, respectively.

96. The apparatus of claim 92, wherein said computing platform is further adapted to:

for 2, assign a unique multi-set comprising doubleton zero.

97. An article comprising:

a file having a named location;

said named location being formed from a numerical pair associated with a natural numeral at least by;

forming said numeral pair so that it includes an index natural numeral corresponding to a non-composite numeral and another numeral that produces said natural numeral when multiplied with said non-composite numeral.

98. The article of claim 97, wherein said named location being formed from a numerical pair further associated with a natural numeral at least by:

said natural numeral that comprises a non-composite numeral being designated by said another numeral of said numeral pair comprising a one numeral.

99. The article of claim 97, wherein said named location being formed from a numerical pair further associated with a natural numeral at least by:

forming a finite multi-set from said numeral pair.

100. The article of claim 99, said named location being formed from a numerical pair further associated with a natural numeral at least by:

manipulating said finite multi-set.

101. The article of claim 100, said named location being formed from a numerical pair further associated with a natural numeral at least by:

forming another finite multi-set from another numeral pair;

wherein manipulating said finite multi-set comprises;

combining said finite multi-sets.

102. The article of claim 101, wherein said named location being formed from a numerical pair associated with a natural numeral at least by:

said combining said finite multi-sets comprising multiplying the associated natural numerals.

103. The article of claim 101, wherein said named location being formed from a numerical pair further associated with a natural numeral at least by:

said combining said finite multi-sets comprising merging the associated numeral pairs.

104. The article of claim 97, said named location being formed from a numerical pair further associated with a natural numeral at least by:

associating another natural numeral with another numeral pair; and

multiplying natural numerals by merging associated numeral pairs.

105. The article of claim 104, wherein said named location being formed from a numerical pair further associated with a natural numeral at least by:

said merging numeral pairs comprising combining [a,b] with [c,d] as follows;

[a, b*Q(c)″

*d], in which “

*”

represents multiplication and where the function Q(c) is a function that provides the non-composite numeral associated with the index c, as for the Kleene enumeration.

106. The article of claim 104, wherein said named location being formed from a numerical pair further associated with a natural numeral at least by:

said numeral pairs being represented as binary numerals, and multiplying said natural numerals using the same or fewer bits than associated with binary representations of said natural numerals by merging the binary numeral pairs.

107. The article of claim 97, wherein said named location being formed from a numerical pair further associated with a natural numeral at least by:

said natural numeral being represented by a binary numeral representation of said numeral pair.

108. An apparatus comprising:

a computing platform;

said computing platform being adapted to associate a natural numeral with a numeral pair as follows;

forming said numeral pair so that it includes an index natural numeral corresponding to a non-composite numeral and another numeral that produces said natural numeral when multiplied with said non-composite numeral.

109. The apparatus of claim 108, wherein said computing platform being further adapted to associate a natural numeral with a numeral pair by said natural numeral that comprises a non-composite numeral being designated by said another numeral of said numeral pair comprising a one numeral.

110. The apparatus of claim 108, wherein said computing platform is further adapted to form a finite multi-set from said numeral pair.

111. The apparatus of claim 110, wherein said computing platform is further adapted to manipulate said finite multi-set.

115. The apparatus of claim 108, wherein said computing platform is further adapted to associate another natural numeral with another numeral pair;

and to multiply the natural numerals by merging associated numeral pairs.

116. The apparatus of claim 115, wherein said computing platform is further adapted to combine [a,b] with [c,d] as follows:

[a, b*Q(c)″

*d], in which “

*”

represents multiplication and where the function Q(c) is a function that provides the non-composite numeral associated with the index c, as for the Kleene enumeration.

117. The apparatus of claim 115, wherein said computing platform is further adapted to represent said numeral pairs as binary numerals:

and to multiply said natural numerals using the same or fewer bits than associated with binary representations of said natural numerals by merging the binary numeral pairs.

118. The apparatus of claim108, wherein said computing platform being adapted to represent said natural numeral by a binary numeral representation of said numeral pair.

119. An apparatus comprising:

a computing platform;

said computing platform adapted to uniquely associate a plurality of natural numerals with a plurality of numeral pairs, wherein at least one of the numerals for each of said pairs represents an index for the Kleene enumeration.

120. The apparatus of claim 119, wherein said computing platform is further adapted to uniquely associate a plurality of finite multi-sets with said natural numerals and said numeral pairs.

121. The apparatus of claim 120, wherein said computing platform is further adapted to associate, for the numerals 0, 1, and 2, the multi-sets, the empty set, singleton zero and doubleton zero respectively.

122. The apparatus of claim 121, wherein computing platform is further adapted to associated, for composite numerals, 2K, the multi-set comprising a merger of singleton zero with the multi-set associated with K.

123. The apparatus of claim 122, wherein said computing platform is further adapted to associate, for composite numerals, K*L, the multi-set comprising a merger of the multi-set associated with K with the multi-set associated with L.

124. An article comprising:

a file;

said file having a named location;

said named location being part of a file location naming hierarchy formed at least by;

associating a plurality of natural numerals with a plurality of numeral pairs, wherein at least one of the numerals for each of said pairs represents an index for the Kleene enumeration.

125. The article of claim 124, wherein said file location naming hierarchy is further formed by:

uniquely associating a plurality of finite multi-sets with said natural numerals and said numeral pairs.

126. The article of claim 125, wherein said file location naming hierarchy is further formed by:

associating, for the numerals 0, 1, and 2, the multi-sets the empty set, singleton zero and doubleton zero, respectively.

127. The article of claim 126, wherein said file location naming hierarchy is further formed by:

associating, for composite numerals 2K, the multi-set comprising a merger of singleton zero with the multi-set associated with K.

128. The article of claim127, wherein said file location naming hierarchy is further formed by:

associating, for composite numerals K*L, the multi-set comprising a merger of the multi-set associated with K with the multi-set associated with L.

129. An article comprising:

a file;

said file having a named location;

said named location being part of a binary tree file location naming hierarchy at least formed from a finite multi-set by;

associating said finite multi-set with a natural numeral; and

associating a first non-composite numeral and a second non-composite numeral with said natural numeral, said non-composite numerals and said finite multi-set forming at least a portion of said hierarchy.

130. The article of claim 129, wherein said file location naming hierarchy is further formed by:

said finite multi-set representing a named location for a file in said hierarchy, and said first and second non-composite numerals representing additional named locations for related files in said hierarchy.

131. The article of claim 129, wherein said file location naming hierarchy is further formed by:

associating a plurality of binary trees with finite multi-sets, each binary tree associated with a finite multi-set further associated with two or more natural numerals larger than one.

132. An apparatus comprising:

a computing platform;

said computing platform adapted to form a binary tree file location naming hierarchy from a finite multi-set as follows;

associating said finite multi-set with a natural numeral;

associating a first non-composite numeral and a second non-composite numeral with said natural numeral, said non-composite numerals and said finite multi-set forming at least a portion of said hierarchy.

133. The apparatus of claim 132, wherein said computing platform being further adapted to represent a named location for a file in said hierarchy with said finite multi-set, and to represent additional named locations for related files in said hierarchy with said first and second non-composite numerals.

134. The apparatus of claim 132, wherein said computing platform is further adapted to associate a plurality of number of binary trees with finite multi-sets, each binary tree associated with a finite multi-set further associated with two or more natural numerals larger than one.

135. An article comprising:

a plurality of files;

said files having a named location in a file location naming hierarchy;

said hierarchy being formed at least by;

associating at least some files of said file location naming hierarchy with non-composite numerals.

136. The article of claim 135, wherein said hierarchy is further formed at least by:

associating said at least some files in said file location naming hierarchy with non-composite numerals and/or products of non-composite numerals; and

wherein at least some files in said hierarchy are moved between by;

dividing and/or multiplying said non-composite numerals and/or associated products with non-composite numerals.

137. The article of claim 136 wherein said hierarchy is further formed at least by:

said associating comprising associating other files other than said at least some files with non-composite numerals.

138. The article of claim 137, wherein at least some files in said hierarchy are moved between by:

dividing and/or multiplying with non-composite numerals.

139. The article of claim 136, wherein said hierarchy is further formed at least by:

said associating comprising associating said at least some files with non-composite numerals; and

wherein at least some files in said hierarchy are moved between by;

multiplying and/or dividing by a non-composite numeral.

140. An apparatus comprising:

a computing platform;

said computing platform being adapted to;

associate at least some files of a file location naming hierarchy with non-composite numerals.

141. The apparatus of claim 140, wherein said computing platform is further adapted to associate said at least some files in said file location naming hierarchy with non-composite numerals and/or products of non-composite numerals;

and is further adapted to move between said at least some files by dividing and/or multiplying said non-composite numerals and/or associated products with non-composite numerals.

142. The apparatus of claim 141, said computing platform is further adapted to associate other files other than said at least some files with non-composite numerals.

143. The apparatus of claim 142, said computing platform is further adapted to move between said at least some files by dividing and/or multiplying with non-composite numerals.

144. The apparatus of claim 141, wherein said computing platform is further adapted to associate said at least some files with non-composite numerals;

and further adapted to movie between said at least some files by multiplying and/or dividing by a non-composite numeral.

145. An apparatus comprising:

means for forming a file location naming hierarchy;

wherein said hierarchy comprises at least a multi-set (MS) of a set of elements; and

means for accessing a file in said hierarchy.

146. The apparatus of claim 145, wherein said MS of a set of elements comprises a MS of a MS of said set of elements.

147. The apparatus of claim 145, wherein said set of elements comprise natural numerals.

148. The apparatus of claim 145, wherein said hierarchy further comprises compound multi-sets of said set of elements.

149. An apparatus comprising:

means for arranging files in a file location naming hierarchy comprising;

means for forming a multi-set from a set of elements; and

means for forming at least one more multi-set from said multi-set;

wherein said hierarchy comprises the multi-sets.

150. The apparatus of claim 149, wherein said means for forming at least one more multi-set comprising means for recursively forming at least one compound multi-set.

151. The apparatus of claim 150, wherein said means for recursively forming at least one compound multi-set comprising means for recursively forming a plurality of compound multi-sets.

152. An apparatus comprising:

means for associating a natural numeral with a multi-set comprising;

means for assigning a unique multi-set, for the numeral 2; and

means for assigning the merger of the multi-set for 2 with the multi-set for K, for even composite numerals 2K.

153. The apparatus of claim 152, and further comprising:

means for assigning additional unique multi-sets, for the numerals 0 and 1; and

means for assigning the associated Kleene enumeration index, for odd non-composite numerals.

154. The apparatus of claim 153, and further comprising:

means for assigning the merger of the multi-set for K with the multi-set for L, for composite numerals K*L.

155. The apparatus of claim 153, wherein said means for assigning additional unique multi-sets comprising means for assigning the empty set and singleton zero, for the numerals 0 and 1, respectively.

156. The apparatus of claim 152, wherein said means for assigning a unique multi-set comprising means for assigning doubleton zero, for the numeral 2.

157. An apparatus comprising:

means for associating a natural numeral with a numeral pair comprising;

means for forming said numeral pair;

said means for forming said numeral pair comprising;

means for including a Kleene enumeration index natural numeral corresponding to a non-composite numeral and means for including another numeral that produces said natural numeral when multiplied with said non-composite numeral.

158. The apparatus of claim 157, and further comprising:

means for designating said natural numeral that comprises a non-composite numeral;

said means for designating comprising means for said another numeral of said numeral pair including a numeral 1.

159. The apparatus of claim 157, and further comprising:

means for forming a finite multi-set from said numeral pair.

160. The apparatus of claim 159, and further comprising:

means for manipulating said finite multi-set.

161. The apparatus of claim 160, and further comprising:

means for forming another finite multi-set from another numeral pair;

wherein said means for manipulating said finite multi-set comprises;

means for combining the finite multi-sets.

162. The apparatus of claim 161, wherein said means for combining the finite multi-sets comprising:

means for multiplying the associated natural numerals.

163. The apparatus of claim 161, wherein said means for combining the finite multi-sets comprising:

means for merging the associated numeral pairs.

164. The apparatus of claim 157, and further comprising:

means for associating another natural numeral with another numeral pair; and

means multiplying the natural numerals comprising means for merging the associated numeral pairs.

165. The apparatus of claim 164, wherein said means for merging the associated numeral pairs comprising:

means for combining [a,b] with [c,d];

wherein said means for combining comprises [a, b*Q(c)″

*d], in which “

*”

represents multiplication and where the function Q(c) is a function that provides the non-composite numeral associated with the index c, as for the Kleene enumeration.

166. The apparatus of claim 164, and further comprising:

means for representing said numeral pairs as binary numerals; and

wherein said means for multiplying said natural numerals including means for merging the binary numeral pairs using the same or fewer bits than associated with binary representations of said natural numerals.

167. The apparatus of claim 157, and further comprising:

means for representing said natural numeral with a binary numeral representation of said numeral pair.

168. An apparatus comprising:

means for uniquely associating a plurality of natural numerals with a plurality of numeral pairs, wherein at least one of the numerals for each of said pairs represents an index for the Kleene enumeration.

169. The apparatus of claim 168, wherein said means for uniquely associating comprises means for uniquely associating a plurality of finite multi-sets with said natural numerals and said numeral pairs.

170. The apparatus of claim 169, and further comprising:

means for uniquely associating, for the numerals 0, 1, and 2, the multi-sets comprising the empty set, singleton zero and doubleton zero, respectively.

171. The apparatus of claim 170, and further comprising:

means for uniquely associating, for composite numerals 2K, the multi-set comprising a merger of singleton zero with the multi-set associated with K.

172. The apparatus of claim 171, and further comprising:

means for uniquely associating, for composite numerals K*L, the multi-set comprising a merger of the multi-set associated with K with the multi-set associated with L.

173. An apparatus comprising:

means forming a binary tree file location naming hierarchy from a finite multi-set comprising;

means for associating said finite multi-set with a natural numeral; and

means for associating a first non-composite numeral and a second non-composite numeral with said natural numeral, said non-composite numerals and said finite multi-set forming at least a portion of said hierarchy.

174. The apparatus of claim 173, and further comprising:

means for representing a named location for a file in said hierarchy with said finite multi-set, and

means for representing additional named locations for related files in said hierarchy with said first and second non-composite numerals.

175. The apparatus of claim 173, and further comprising:

means for associating a plurality of binary trees with finite multi-sets, each binary tree associated with a finite multi-set further associated with two or more natural numerals larger than one.

176. An apparatus comprising:

means for associating at least some files of a file location naming hierarchy with non-composite numerals.

177. The apparatus of claim 176, wherein said means for associating comprising means for associating said at least some files in said file location naming hierarchy with non-composite numerals and/or products of non-composite numerals;

and further comprising;

means for moving between said at least some files including dividing and/or multiplying said non-composite numerals and/or associated products with non-composite numerals.

178. The apparatus of claim 177, wherein said means for associating comprising means for associating other files other than said at least some files with non-composite numerals.

179. The apparatus of claim 178, said means for moving between said at least some files comprising dividing and/or multiplying with non-composite numerals.

180. The apparatus of claim 177, wherein said means for associating comprising means for associating said at least some files with non-composite numerals;

and said means for moving between said at least some files comprising multiplying and/or dividing by a non-composite numeral.