How does one prove the Direct Comparison Test for infinite series?

The wikipedia article is trivial nonsense. The wikipedias "comparison test" has a proof which, as far as I can tell, makes use of the comparison to prove the comparison.
Saying that a_n < b_n and therefore that A_n < B_n is obvious and intuitive, but by no means rigorous.

Consider using A_n < B_n

Here is the link that proves the direct comparison test… http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CCwQFjAC&url=http%3A%2F%2Fplanetmath.org%2Fencyclopedia%2FProofOfLimitComparisonTest2.html&ei=oHPZTvfGB8XL0QHR8ajZDQ&usg=AFQjCNFgmxooNQif6DyVOzD3mg9jUab5MA&sig2=IJtj99zYJEgC-ElpZZfGdg

Good luck!