As a native speaker, I just want to remark that I disagree completely with each of your suggestions to rephrase. If I were the author, I would go on to illustrate my meaning in each of these cases and prod you for information on how I could really improve them, based on whatever unstated misunderstanding is actually troubling you.
But I'm not the author; I'm just an enthusiast of expression in such ways as provided by English and Perl. So, my curiosity is piqued: what is more awkward in the third paragraph of the first chapter than "must compare always two elements"?
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