The Law of Large Numbers

[AWilliams]

Isn't the law of large numbers just an alternative explination for the central limit theorem? Two me, both are the same exact phenomena. If so, why break it up into seperate theorems?
Pardon my ignorance in advance.

 

[Eugene Krel]

http://www.stat.lsa.umich.edu/~kshedden/Courses/Stat406_2006/Stat406/Notes/CLT.pdf

 

[AlexandreH]

http://en.wikipedia.org/wiki/Central_limit_theorem#Relation_to_the_law_of_large_numbers

 

[pruse]

Isn't the law of large numbers just an alternative explination for the central limit theorem? Two me, both are the same exact phenomena. If so, why break it up into seperate theorems?
Pardon my ignorance in advance.

why break it up? because the two are first of all mathematically non-equivalent statements, and second of all are non-trivially different -- well, because they're not equivalent.