Mbachtold

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August 2018

Thank you for your contributions. Please mark your edits as "minor" only if they are minor edits. In accordance with Help:Minor edit, a minor edit is one that the editor believes requires no review and could never be the subject of a dispute. Minor edits consist of things such as typographical corrections, formatting changes or rearrangement of text without modification of content. Additionally, the reversion of clear-cut vandalism and test edits may be labeled "minor". Thank you. –Deacon Vorbis (carbon • videos) 14:16, 28 August 2018 (UTC)

... just to let you know my reply to the reverted comment on "functions of"

Communication via WP articles and comments on TPs employs natural language, interspersed with snippets of formal language. Obviously, this requires readiness to struggle for the meaning of this (Wittgenstein's first attempt on this ended in "silencing"). I see a root of these here troubles in you not extending the referability of names, bounded within one formal snippet, from a local scope to the level of the embedding natural language. A formal definition of a function may bind the name the variable used for its definition to a strictly local scope, nevertheless it is common habit, and to my understanding a good one, to distinctly refer to the variable of a function from outside the snippet via the name bound within. Using both x and y to refer some object f(z) might both be formally correct and paradigmatically bad usability. I think D.Lazard addressed this already with declaration.

If I missed your intentions again, I suggest that you consider the possibility that you resiliently miss to communicate your target. Perhaps it is hidden behind aggressive pity. In any case, when I now write that I stop commenting on this thread, I do mean it. Purgy (talk) 09:58, 1 September 2018 (UTC)

@Purgy: Thank you for your attempts to engage in a reasonable dialogue. I apologize for my agressive tone. I know it is not justified, but I hope it is at least understandable, considering how people have reacted to my edits (asking to call my Randy, ignoring my questions, treating me as though I haven't understood the difference between f and f(x) and immediately reverting without engaging in a dialogue). I also respect that you don't want to continue this discussion any further. Let me nevertheless make a last attempt to explain my point of view, hopefully without aggressive pity. What I am trying to argue is that the interpretation of "something is a function of x" suggested by D. Lazard contradicts the meaning which this phrase has had for the past 300 years of mathematics. This is not a matter of my personal opinion or dispute, it can be seen by reading how people defined the word 'function' since 1715 to roughly 1925 (which is the time around which the modern definition, which calls f the function becomes standard). I quoted 8 such historic definitions (Bernoulli, Euler, Cauchy, Bolzano, Dirichlet, Riemann, Peano and Courant) at the end of my question on Mathoverflow, and could provide more if those are considered to little evidence. In all of them, what's being defined is the meaning of "something is a function of x", and not of "something is a function". And in all of those definitions, what was being called a 'function of x' was f(x), not f. None of those definitions gives f a name or calls it a function (actually Bernoulli, Euler and Lagrange called it the "characteristic of the function f(x)" but almost never used that expression). The fact that people around 1925 decided to call the f a function is a priori not a contradiction to also calling f(x) a function of x, but it makes communication today very hard. (I'm afraid this is part of why my explanations are missing the target.) Maybe it helps to know, that before settling on "function" as name for 'f', Peano, Dedekind and Cantor around 1890 all independently decided to call f something else, like "mapping", "allocation" or "function symbol". For all of them the word function was already attached to f(x) and it was clear that f was something else. This historical perspective also makes it clear why today mathematicians still call sin x or x^2 a function. The reason is that that was correct for 200 years. Actually it would have been correct for Euler, Lagrange etc. to call sin x and x^2 functions of x, but the "of x" was implied from the context or notation, so they just called them functions. The interpretation of "something is a function of x" by D. Lazard is a modern attempt to reinterpret the phrase, but it does not correspond to the established practice. And unfortunately I don't see how to make formal sense of it. On the other hand I do know how to give a formal sense to "x^2 is a function of x".Mbachtold (talk) 11:40, 1 September 2018 (UTC)