In "Evasion differential game of many pursuers and one evader for an infinite system of binary differential equations" the authors present us with a differential game, formally well delineated, which they then solve in Theorem 1 through a constructive proof, in which they create strategies for the evader and the pursuers. Formally, from a mathematical point of view, it seems ok. Now let's look at the problems: -The text is full of grammatical errors: confusion in the use of the comparative and the superlative; wrong subject and verb concordances; words misused,..., In short, it is necessary to carry out a profound revision of English. -The first section, without title, must be titled. I think it would be fine 1. Introduction (the following ones being renumbered accordingly). In this section there is a literature review, very clumsy, uncritical, in which many references appear treated to packages. Possibly, each package could be represented by just one. If not, they cannot be packaged. A thorough review is needed here. Otherwise it seems that the authors just wanted to fill the bibliography. There is also a need to make more comments, and in a critical way. -As for the problem, the center of this text, it is necessary to know if it was created by the authors or inspired by other sources. In any case, a real-life situation must be set that matches the problem (in fact, the authors claim that many real-life situations can formalize these problems). This would help a lot to understand the formalization and to feel better about the strategies created. The blunt presentation of mathematical formalization fails on these points and is a disincentive to readers. Without these corrections, it is very difficult to make a correct assessment of the paper, and to give an opinion on its possible publication in Mathematics.

The text has evidently improved, not as much as I would have liked, but enough that it could be published in Mathematics. I only asked the authors to give due prominence to their main result.