Fun with Math

11 Responses to “Fun with Math”

1. 
   Max Beauchez
   September 18th, 2006 at 12:59 pm

   ROFLASTD! (rolling on the floor laughing and scaring the dog, for the n00bs )

2. 
   desrt
   September 18th, 2006 at 12:59 pm

   lim (x->8) 1/(x-8) is not infinity. it does not exist.

3. 
   jamin
   September 18th, 2006 at 5:50 pm

   desrt: yes it is. The limit of 1/(x-8) as x approaches 8 is infinity.

4. 
   Tristan
   September 18th, 2006 at 6:13 pm

   No, it’s not. As desrt says, it doesn’t exist. Draw the graph; it shoots off in different directions depending on whether you approach 8 from the left or from the right. To have a defined limit, you’d need to take the absolute value, i.e. lim(x->8) 1/|x-8|

   Of course, you can get round this by declaring x to belong to the one-point compactification of the real line, but I think that’s what was meant…

5. 
   desrt
   September 18th, 2006 at 6:37 pm

   definitely not.

   a limit as (x->h) f(x) is only defined if 3 conditions hold:

   lim (x->h ) f(x) is defined
   lim (x->h-) f(x) is defined
   lim (x->h ) f(x) == lim (x->h-) f(x)

   in this case:

   lim(x->8 ) 1/(x-8) = inf
   lim (x->8-) 1/(x-8) = -inf

   think about:

   1/(7.9999999-8) = 1/(small negative number) = -inf
   1/(8.0000001-8) = 1/(small positive number) = inf

   so lim(x->8) 1/(x-8) does not exist.

6. 
   desrt
   September 18th, 2006 at 6:39 pm

   oh no! your blog ate all of my plus symbols.

   if you see lim (x->h[space]) i actually said (x->h[plus])

7. 
   tm
   September 19th, 2006 at 2:52 am

   Here are some more mathematical jewels - the last one, in my opinion, is the best:
   http://klab.lv/community/lol/733267.html

8. 
   tm
   September 19th, 2006 at 2:54 am

   oh hell, sorry, didn’t check the link on top

9. 
   jamin
   September 20th, 2006 at 9:06 pm

   Thanks for the refresher on limits. It’s been too long…

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