Timeline for When did the abuse of notation $y=y(x)$ start?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 2, 2016 at 13:13 | comment | added | Mauro ALLEGRANZA | And see page 6 : "let $o$ be a very small Quantity, and let $oz, oy, ox$ be the Moments, that is the momentaneous synchronal increments of the Quantities $z, y, x$. And if the flowing Quantities are just now $z, y, x$, then after a Moment of Time, being increas'd by their Increments $oz, oy, ox$, these Quantities shall become $z+o \dot z,y + o \dot y, x + o \dot x$". 3/3 | |
| Nov 2, 2016 at 13:10 | comment | added | Mauro ALLEGRANZA | ...I sought a Method of determining Quantities from the Velocities of the Motions or Increments, with which they are generated ; and calling these Velocities of the Motions or Increments Fluxions [$\dot x$], and the generated Quantities Fluents [$x$]." 2/3 | |
| Nov 2, 2016 at 13:08 | comment | added | Mauro ALLEGRANZA | Newton is not so "explicit" but, due to his "dynamical intended interpretation" of the calculus, it is correct to say that the "independent variable" is time. See : Treatise of the Quadrature (1st ed 1710), page 1 : "considering that Quantities, which increase in equal Times, and by increasing are generated, become greater or less according to the greater or less Velocity with which they increase and are generated; 1/3 | |
| Nov 2, 2016 at 10:00 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
Fixed LaTeX on 'x-axis'
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| Nov 1, 2016 at 18:13 | comment | added | Michael Bächtold | Maybe this answer helps to understand the distinction between a function and a variable (which I find very relevant for such discussions): math.stackexchange.com/a/1259113/1984 | |
| Nov 1, 2016 at 16:19 | comment | added | Amir Asghari | I cannot see how Newton could calculate $\dot x$ without thinking of $x$ as $x(t)$, though he never wrote something like $x=x(t)$. In fact, that is why I added that comment, because the separation you have made would be only possible after having the modern definition of function. | |
| Nov 1, 2016 at 15:56 | comment | added | Michael Bächtold | Thanks for you attempt to answer this, unfortunately I don't see why that quote of Newton is an example of what I'm asking for. Concerning you last paragraph, I understand that one may argue that writing y=y(x) is not technically an abuse of notation, but if you think of the y on the right as a distance, (which is not a function of type $\mathbb{R}\to\mathbb{R}$) then you are abusing the notation for function application. | |
| Nov 1, 2016 at 15:12 | history | answered | Amir Asghari | CC BY-SA 3.0 |