Stacked fractions: Difference between revisions

From Why start at x, y, z
No edit summary
(Added reference for convoluted example due to Barry Mazur who was trying to annoy Serge Lang.)
 
(2 intermediate revisions by one other user not shown)
Line 1: Line 1:
[[Category:Ambiguities]]
[[Category:Ambiguities]]
[[Category:Handwriting]]


A fraction written on multiple levels is often ambiguous, especially when handwritten. For example, \(\frac{10}{\frac{2}{5}}\) and \(\frac{\frac{10}{2}}{5}\) result in 25 and 1, respectively.
A fraction written on multiple levels is often ambiguous, especially when handwritten. For example, \(\frac{10}{\frac{2}{5}}\) and \(\frac{\frac{10}{2}}{5}\) result in 25 and 1, respectively.


Things get even worse when you use the letter \(\Xi\) in this convoluted example:
Things get even worse when you use the letter \(\Xi\) in this convoluted example<ref>[http://www.ams.org/notices/200605/fea-lang.pdf AMS Notices: Remembrances of Serge Lang]</ref>:


\[ \frac{\Xi}{\bar\Xi} \]
[[File:Xi bar over Xi .jpg|thumb|center|alt=A handwritten stacked fraction with Xi bar divided by Xi. In effect it looks like nothing more than a stack of eight horizontal lines of varying sizes.|\(\frac{\bar \Xi}{\Xi}\), handwritten]]
 
[[File:Xi bar over Xi .jpg|thumb]]

Latest revision as of 16:38, 12 July 2021


A fraction written on multiple levels is often ambiguous, especially when handwritten. For example, \(\frac{10}{\frac{2}{5}}\) and \(\frac{\frac{10}{2}}{5}\) result in 25 and 1, respectively.

Things get even worse when you use the letter \(\Xi\) in this convoluted example[1]:

A handwritten stacked fraction with Xi bar divided by Xi. In effect it looks like nothing more than a stack of eight horizontal lines of varying sizes.
\(\frac{\bar \Xi}{\Xi}\), handwritten