Question

Given two lists A={a1,a2,a3,...an} and B={b1,b2,b3,...bn}, I would say A>=B if and only if all ai>=bi.

There is a built-in logical comparison of two lists, A==B, but no A>B.
Do we need to compare each element like this

And@@Table[A[[i]]>=B[[i]],{i,n}]

Any better tricks to do this?

EDIT:
Great thanks for all of you.

Here’s a further question:

How to find the Maximum list (if exist) among N lists?

Any efficient easy way to find the maximum list among N lists with the same length using Mathematica?

Answer 1

Method 1: I prefer this method.

NonNegative[Min[a - b]]

Method 2: This is just for fun. As Leonid noted, it is given a bit of an unfair advantage for the data I used.
If one makes pairwise comparisons, and return False and Break when appropriate,
then a loop may be more efficient (although I generally shun loops in mma):

result = True;
n = 1; While[n < 1001, If[a[[n]] < b[[n]], result = False; Break[]]; n++]; result

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Some timing comparisons on lists of 10^6 numbers:

a = Table[RandomInteger[100], {10^6}];
b = Table[RandomInteger[100], {10^6}];

(* OP's method *)
And @@ Table[a[[i]] >= b[[i]], {i, 10^6}] // Timing

(* acl's uncompiled method *)
And @@ Thread[a >= b] // Timing

(* Leonid's method *)
lessEqual[a, b] // Timing

(* David's method #1 *)
NonNegative[Min[a - b]] // Timing

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Edit: I removed the timings for my Method #2, as they can be misleading. And Method #1 is more suitable as a general approach.