Timeline for Most harmful heuristic?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2021 at 19:30 | history | edited | sɪʒɪhɪŋ βɪstɦa kxɐll | CC BY-SA 4.0 |
fixed grammar, improved formatting
|
| Aug 25, 2017 at 22:54 | comment | added | Anton Fetisov | putting on my constructivist hat Well if you define a function over the naturals by its values for odd and even numbers, then you must prove that this indeed defines a function for all $n:\mathbb N$. Some people can even claim this way that there are discontinuous functions $\mathbb R \to \mathbb R$! | |
| Nov 4, 2016 at 18:13 | comment | added | LSpice | @AmritanshuPrasad, I agree with you. I was just joking. | |
| Nov 4, 2016 at 8:55 | comment | added | Amritanshu Prasad | @LSpice My comment was not an answer to the question, in the sense that this definition is not a heuristic. It registers my disagreement with Qiaochu;s answer. My point is that sometimes functions should be thought of as formulas, rather than as relations of a special kind, and this is something that mathematicians often do (for example when we talk about formal power series or polynomials as functions). | |
| Oct 20, 2016 at 18:39 | comment | added | LSpice | @AmritanshuPrasad, are you saying that doesn't match your intuitive picture of a function? This sort of intuitive friendliness is why I define a partial function as the converse of an injective relation; it's so much clearer that way. | |
| Oct 20, 2016 at 18:05 | comment | added | Amritanshu Prasad | Much worse than this heuristic is the "official" definition of a function $X\to Y$ as a subset of $X\times Y$ satisfying various axioms. | |
| Oct 20, 2016 at 9:56 | comment | added | Kolya Ivankov | That's precisely the Euler view: in his works, "continuous functions" were those you may write with a single analytic expression. So 1/x was continuous, while "0 for $x<0$, $x$ for $x\ge 0$" wasn't. | |
| May 28, 2015 at 21:06 | comment | added | Michael | Moreover, even for the best of mathematicians on 18th and much of 19th century "function" meant "analytic function"... | |
| Jan 27, 2012 at 8:31 | comment | added | Elizabeth S. Q. Goodman | Actually I still have a lot of trouble going back the other way, to "functions are polynomial formulas, not maps" in algebraic geometry and/or combinatorics. | |
| Apr 25, 2010 at 22:21 | comment | added | Christopher Olah | <p> I'm a high school student and I can safely say that most of my peers just don't get what a function is. The only ones who do seem to have learned from programing. Then again, all the really mathematically talented students in my very small school also program... </p> <p>Functions seem to get slipped in somewhere along the line without a proper introduction, and then it is assumed that students know it from there on in.</p> | |
| Apr 25, 2010 at 19:06 | comment | added | Qfwfq | I think that by the second year of high school normally smart students should perfectly get the point with this. | |
| Oct 24, 2009 at 21:27 | comment | added | Michael Hoffman | I think this actually comes up even as late as upper division linear algebra, when they start to talk about general linear transforms, or, something even harder for students, the space of linear transforms from V to W. I worked with a student for quite a long time on this | |
| Oct 24, 2009 at 21:19 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |