> The code is not transformative because the quoted code is not used for some other purpose like as part of an article discussing whatever the code does, it is used to do exactly it's original job.
Hmm..
> The printing press is not transformative because the printed text is not used for some other purpose, it is used to do exactly it's original job.
See the error in your logic? The potentially transformative part is not the code itself. It's the impact to the process of creating the code.
> Most often it is not necessary, and not wanted, to enforce a and b having the same type.
That really depends on what you're trying to do. Presenting these two different declarations as somehow equivalent is very misleading and I'm glad that the author didn't do that.
> * I find it quite unusual in practice for genuinely new symbolic notation to be introduced by an author.
This sentence seems to contradict the rest of your comment; did you mean "I find it quite unusual in practice for genuinely new symbolic notation to NOT be introduced by an author."?
> They are nested in a physical sense, its simply not valid html.
For this to be true, you'd need containment to be a nontransitive relationship. In the sense in which h3 #2 is contained within h3 #1, all of the following hold:
> If multiplication can be sometimes commutative and sometimes non-commutative (and it can, and it is) then why cannot addition be sometimes commutative and sometimes non-commutative?
To which I reiterate my response: because addition in plain English is frequently (if not always?) commutative, whereas multiplication in plain English is frequently NOT commutative (even though it sometimes can be).
>is in some sense a single value. In another sense, it is two values.
What I tryed to say is that the sense in which “exactly one element” is used in the definition of function is inclusive of codomain being R^n, so it confused me why you would provide a function that has a codomain of R^2 as something that suggests deviation from the formalism. It just seemed misleading to phrase it that way
I thought consistently would convey the idea I had, nevermind if it doesn’t
My bad about bijectivity, I see it now, you’re right
Which is clearly not what you mean. I'm not asking about what it means, but about a reference. I teach calculus for a living, and I make a big deal about the two meanings of this word, but never found a definitive reference to cite.
This is a new example. How does that contradict any of the previous points that I (and the OP) made? I fail to see that, can you explain?
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