Timeline for Variable-centric logical foundation of calculus
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Jul 2 at 2:01 | answer | added | user76284 | timeline score: 1 | |
| Jun 25 at 6:04 | comment | added | Alexey Muranov | @LSpice, I thought so too, but this is an error, $d$ is not a binder, $dx$ is a differential of $x$, that's it. I explained more here. Modern undergraduate calculus is a strange creation of Frankenstein. | |
| Jun 24 at 23:05 | comment | added | LSpice | @AlexeyMuranov, re, I think that it is almost universally correct, in the context of undergraduate calculus, to regard the "$\mathrm dx$" in $\int x\mathrm dx$ (as opposed to in, say, $\frac{\mathrm d(x^2)}{\mathrm dx}$) as a binder, so that the $x$ is no longer free. | |
| Jun 24 at 14:37 | answer | added | Alexey Muranov | timeline score: 2 | |
| Feb 25, 2023 at 21:27 | comment | added | Alexey Muranov | @CarlMummert, if I understand correctly that you were looking for formal rules telling which variable is bound in which expression, then those are not given for a good reason: you cannot tell by looking at the expression alone. For example, in "$\int_0^1 xdx$", the variable $x$ could be bound or free at will. If it is free, and the integration variable is $y$, then $\int_0^1 xdx =\int_{y=0}^1 xdx = 0$. Otherwise, $\int_0^1 xdx =\int_{x=0}^1 xdx = 1/2$. | |
| Aug 14, 2018 at 4:59 | history | edited | Martin Sleziak |
added some calculus-related tags
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| Aug 13, 2018 at 18:25 | comment | added | Michael Bächtold | @LSpice ... and a lost train of thought. ;) | |
| Aug 13, 2018 at 13:32 | comment | added | LSpice | @MichaelBächtold, and … what? | |
| Aug 13, 2018 at 12:57 | history | edited | Martin Sleziak |
Removed the (tag-removed) tag (The question has been bumped anyway - by an edit on an answer.)
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| Aug 13, 2018 at 7:10 | comment | added | bof | I vaguely recall from browsing Karl Menger's Calculus in a bygone century that it had a lot to say about variables. Don't recall exactly what. | |
| Aug 13, 2018 at 5:26 | answer | added | Mike Shulman | timeline score: 16 | |
| Aug 12, 2018 at 17:58 | comment | added | Michael Bächtold | Two related questions: If d/dx is an operator, on what does it operate? and Formalizations of the idea that something is a function of something else and | |
| Dec 7, 2012 at 1:54 | answer | added | Todd Trimble | timeline score: 8 | |
| Dec 6, 2012 at 4:15 | answer | added | Andrej Bauer | timeline score: 17 | |
| Dec 6, 2012 at 4:04 | comment | added | Carl Mummert | I have never seen a calculus book that treats the variables properly, e.g. by giving a proper definition of which variables are bound in each expression. | |
| Dec 6, 2012 at 0:37 | comment | added | David Roberts♦ | @Gerry, maybe not yet. See ncatlab.org/schreiber/show/… | |
| Dec 6, 2012 at 0:27 | answer | added | Joel David Hamkins | timeline score: 11 | |
| Dec 24, 2011 at 16:24 | comment | added | Gerry Myerson | I imagine that by this point, every conceivable logical foundation for Calculus has been explored to within an inch of its life. Don't take what you see in the textbooks as indicative of what's in the journals and monographs. | |
| Dec 24, 2011 at 15:23 | history | asked | Jason Howald | CC BY-SA 3.0 |