Suppose I have a string of inequalities, i.e. f ( x , y , z...

Jonathan Miles

Jonathan Miles

Answered

2022-07-04

Suppose I have a string of inequalities, i.e.
f ( x , y , z ) < g ( x , y , z ) < h ( x , y , z )
Clearly, if I find when g ( x , y , z ) < h ( x , y , z ) and f < g, then f < h when both these conditions hold.
Is it ever useful to compare f ( x , y , z ) < h ( x , y , z ) in addition to f < g and g < h
Or is it useful to compare the conditions (assuming I can get them in a comparable form) from g < h and f < h to each other? Maybe comparing the two can give a single, simplified condition for f < g < h to hold?

Answer & Explanation

Jamiya Costa

Jamiya Costa

Expert

2022-07-05Added 18 answers

Note that
f ( x , y , z ) < g ( x , y , z ) < h ( x , y , z )
is equivalent to the following system
- f ( x , y , z ) < g ( x , y , z )
- g ( x , y , z ) < h ( x , y , z )
and the condition f ( x , y , z ) < h ( x , y , z ) is implicitely assumed by the system.

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