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This commentary considers non-standard analysis and a recently introducedcomputational methodology based on the notion of \G1 (this symbol is called\emph{grossone}). The latter approach was developed with the intention to allowone to work with infinities and infinitesimals numerically in a uniquecomputational framework and in all the situations requiring these notions.Non-standard analysis is a classical purely symbolic technique that works withultrafilters, external and internal sets, standard and non-standard numbers,etc. In its turn, the \G1-based methodology does not use any of these notionsand proposes a more physical treatment of mathematical objects separating theobjects from tools used to study them. It both offers a possibility to createnew numerical methods using infinities and infinitesimals in floating-pointcomputations and allows one to study certain mathematical objects dealing withinfinity more accurately than it is done traditionally. In these notes, weexplain that even though both methodologies deal with infinities andinfinitesimals, they are independent and represent two different philosophiesof Mathematics that are not in a conflict. It is proved that texts\cite{Flunks, Gutman_Kutateladze_2008, Kutateladze_2011} asserting that the\G1-based methodology is a part of non-standard analysis unfortunately containseveral logical fallacies. Their attempt to prove that the \G1-basedmethodology is a part of non-standard analysis is similar to trying to showthat constructivism can be reduced to the traditional mathematics.

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Independence of the grossone-based infinity methodology from  non-standard analysis and comments upon logical fallacies in some texts  asserting the opposite