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Next: 2.12.3 Systems Up: 2.12 Property Tracking Previous: 2.12.1 Properties

2.12.2 Interval Inclusion and Extension

The number system tex2html_wrap_inline33469 , which uses tex2html_wrap_inline33471 to track tex2html_wrap_inline33415 , will be used in the definitions that follow. The value of tex2html_wrap_inline33415 for tex2html_wrap_inline33477   is specified by tex2html_wrap_inline33479 . For tex2html_wrap_inline33481 , tex2html_wrap_inline33483 and tex2html_wrap_inline33485 . When an interval has several properties, a specific property may be referenced by giving its label:   tex2html_wrap_inline33487 references the continuity property, for example.

A model tex2html_wrap_inline33489 of the m-ary function g satisfies the tex2html_wrap_inline33415 inclusion property if for all appropriate tex2html_wrap_inline33497 , tex2html_wrap_inline33161 , and tex2html_wrap_inline32213 :

math8644

To fully satisfy the inclusion property, the model tex2html_wrap_inline33489 must also satisfy the value inclusion property. The value inclusion property is defined as before.

The interval tex2html_wrap_inline33415 extension of the m-ary function g is defined as:

math8655

where tex2html_wrap_inline33511 and tex2html_wrap_inline33513 are:

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The interval value extension is defined as before. The interval extension tex2html_wrap_inline33515 of g is both the interval value extension and the interval tex2html_wrap_inline33415 extension.


next up previous notation contents
Next: 2.12.3 Systems Up: 2.12 Property Tracking Previous: 2.12.1 Properties
Jeff TupperMarch 1996