Timeline for Most harmful heuristic?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2016 at 17:09 | comment | added | Michael Maloney | The point is that you can't combine them as like terms, being inherently unlike. In other words, there is no solution (the the free abelian group of fruit) to the question 3 |apple> + 2 |orange> = 5 |x>. This is far from being harmful, as every elementary algebra teacher knows and as every intro quauntum mechanics professor knows. | |
| Apr 13, 2016 at 1:10 | comment | added | Chris Rackauckas | I'd like to add that this comes up in differential geometry as well. When trying to define the covariant derivative, the intuitive idea of a limit doesn't make sense since you'd have to subtract vectors from different tangent spaces. In this sense, they are in different spaces and so it is like subtracting an apple from an orange. But if you define a connection between tangent spaces, and once you have that connection, you get a lot of powerful geometric objects that make rigorous this idea. So indeed, you cannot add apples and oranges.. until you find out how to relate apples and oranges. | |
| May 29, 2015 at 2:29 | comment | added | Paul Siegel | Isn't the saying "you can't compare apples and oranges"? I'm not aware of a natural order structure on the free abelian group generated by an appl and an orange. | |
| Feb 15, 2015 at 19:59 | comment | added | Matemáticos Chibchas | Well, in the usual math notation, two apples plus three oranges can be written explicitly as $2e_{\mathrm{apple}}+5e_{\mathrm{orange}}$... | |
| Feb 15, 2015 at 4:59 | comment | added | Gerry Myerson | Just occurred to me to wonder whether we shouldn't be adding apples and oranges in the free abelian grape. | |
| Apr 17, 2013 at 19:59 | comment | added | Todd Trimble | So according to Steven's remark, there is of course a universal way to add apples and oranges. (If this observation is not in Mathematics Made Difficult, then it ought to be.) | |
| Oct 2, 2010 at 23:59 | comment | added | Steven Gubkin | Indeed. Take the free abelian group A generated by the set of all types of fruit and consider the natural homomorphism onto the free abelain group generated by {Fruit} induced by sending each generator of A to the single generator of <Fruit> ... | |
| Aug 19, 2010 at 5:50 | comment | added | Gerry Myerson | Two apples plus three oranges equals five pieces of fruit. What's the problem? | |
| Oct 25, 2009 at 2:13 | comment | added | GMRA | This almost belongs in the mathematical jokes question. ;) | |
| Oct 24, 2009 at 21:39 | history | answered | Dave Penneys | CC BY-SA 2.5 |