COUNTER-INTUITIVE?
There are several places in mathematics where ‘the truth’ isn’t quite what it might feel like it should be. This is obviously good and bad.
On the one hand, I’m VERY aware -from years of teaching- that this phenomenon can be frustrating, and contribute to the all-too-familiar feeling that math is just a set of rules that make no sense. 🙁
On the other hand, ‘well informed is well armed’ as they say, and it can help not to be misled, intentionally or otherwise. (See Example 3, e.g.) Intuition can be a valuable ally or a tricky foe.
I’ve picked 3 (of many), interesting* examples of areas where ‘the truth’ is counter-intuitive. The first 2 are related to probability (likelihood), and are prompted by our ‘how likely?’ discussions of earlier this month. The 3rd is DEFINITELY an area where a consumer can be tricked, if not careful.
*I know ‘interesting’ is in the eye of the beholder, but I hope you’ll think so, too. 🙂
To see the three examples, see Counter-Intuitive Examples.