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Next: 2.12 Property Tracking Up: 2.11 Interval Function Domains Previous: 2.11.4 Conjunctions

2.11.5 Simplicity

A simple interval arithmetic which handles partial functions gracefully is
  tex2html_wrap_inline33381 :

math8533

This is not an utter abuse of notation, as tex2html_wrap_inline33387 for any tex2html_wrap_inline33389 : every member of tex2html_wrap_inline33391 may be described as a member of tex2html_wrap_inline31185 . Furthermore, any non-trivial tex2html_wrap_inline33199 warrants the full descriptive power of tex2html_wrap_inline31185 . A trivial tex2html_wrap_inline33199 may be simulated by appropriately constructing tex2html_wrap_inline33401 models.

Consider the square root operator, denoted here as g. It is a unary partial function, undefined for negative arguments. Consider using tex2html_wrap_inline33099 : tex2html_wrap_inline33407 is undefined if j contains only negative numbers. Consider the following examples:

math8541

math8548

This illustrates one approach implementations may take when confronted with partial functions. Another approach is shown in the next section. Another pair of examples follow:

math8559

math8568


next up previous notation contents
Next: 2.12 Property Tracking Up: 2.11 Interval Function Domains Previous: 2.11.4 Conjunctions
Jeff TupperMarch 1996