/sci/ - Science & Math

>>15169079
FTA:
>ZFC has one major flaw: Its use of the word ‘set’ conflicts with how most mathemati- cians use it.
>The root of the problem is that in the framework of ZFC, the elements of a set are always sets too. Thus, given a set X, it always makes sense in ZFC to ask what the elements of the elements of X are. Now, a typical set in ordinary mathematics is R. But ask a randomly-chosen mathematician, ‘what are the elements of π?’, and they will probably assume they misheard you, or tell you that your question makes no sense.
The way this is written is fairly naive. The author is claiming that "ZFC can use the word set" and this suggests that the underlying issue of standardization isn't being manifested. The author isn't dominating the sentences in a way that is directly addressing the relevant issues but rather is imagining things that aren't (that abstract concepts can use words). So we can't have a real conversation about these hallucinations because they aren't real. Also, the elements of pi are simply the Cauchy sequences that converge to pi.
The data abstraction issues are a topic of CS and Abelson and Sussman, not math.
Author hasn't demonstrated a threshold need to drag data abstraction into the conversation, it's a non-sequitur.
Author suggests that readers aren't familiar with data abstraction issues, ignoring relevant CS thought on the topic.
Author is tilting at windmills.
Author is Don Quixote.