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You're right, it's not really the product of some set "G" with itself but hooooo boy a programming/hacker forum is probably the wrong place to be defending the syntax of mathematical notation



If anything, programmers should (and often do!) complain that mathematical notation and terminology isn't defined rigorously enough, and that the main justification for many design decisions is “hysterical raisins”. By comparison, even the wackiest programming languages are the parangon of consistency - after all, they have to be interpreted by machines that can only follow rules.


I'm reading a disagreement in your phrasing, but I think we're saying the same thing: Math notation is the wild west, dressed in the veneer of consistency but indignant at any untoward implication.

Programming languages are praised by their elegance and economy, even when they're wacky. Any theory (programmatic, mathematical, scientific) benefits from those qualities, because theories like to be axiomatic and terse. But any primer or intro or lesson is made MUCH better through repetition and redundancy. Computers don't need the rule of three, people do, and there's an mismatch.


Yes, there's a disagreement. contravariant's complaint about the notation G^2 is completely justified.


I would object too, but I don't see how that could be confusing moreso than any whiteboard "you get what I mean" pseudocode.

The reader's walking in with knowledge of the product-based construction of N-dimensional space, and we readily admit that "R^2" is (a set literally, but) taken to mean the space equipped with whatever operations appropriate for whatever algebra.

I'm being kinda sophist on this. "G^2" isn't meaningful. I agree. But given the convention of naming a set with the implication of whatever topology/metric/norm, the notation is already under harsh torture, right..?


In my reply to contravariant, I explain why I don't think R^2 constitutes abuse of notation: https://news.ycombinator.com/item?id=13241874 .




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