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Homework Statement
Suppose you have a collection of functions [itex]{f_1,f_2,\ldots,f_m}[/itex] and you make the following statement: [itex] f_k ≤ 0[/itex] for all k with strict inequality for at least some k.
Homework Equations
The negation of the above statement is [itex] \exists k [/itex] such that [itex] f_k>0 [\itex].
The Attempt at a Solution
Does the negation of the statement above impose any restriction on the remaining functions (other than [itex]f_k[/itex]? or I am free to assume anything about these other functions?