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efficiently testing a list


Consider the list of pairs:

List = Table[ {a[i],b[i]} , {i,1,N} ].

or

List = { {a[1],b[1]} , {a[2],b[2]} , {a[3],b[3]} , ... ,
{a[N],b[N]} },

and a given function f[a].

What is the quickest way of testing if all elements of List satisfy
f[a[i]] < b[i].




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