Given two sequences of real numbers such as $ a_k<b_k $ what can be said about $\prod_{k=1}^n a_k < \prod_{k=1}^n b_k $. I tried for some values and it seemed like it is true for every positive real number, false for $0$, and only true for negative numbers so that the first condition holds for absolute value too...
2026-04-01 19:13:48.1775070828
Product given two sequences of numbers
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If you have an odd number of negative multiplicands, then the result will be that eventually $\prod a_k >\prod b_k$. If you have an even number of negative multiplicands (including zero negative multiplicands), then the result will be that $\prod a_k < \prod b_k$. If $0$ factors in anywhere of course the result will be false.