does playing with a lower rated players increase your playing ability?

I'm always confused by statements like this.

Chess is a two player game. Both can't be superior, only one of them can. if everybody plays only higher rated players, nobody would ever play, because your higher rated opponent wouldn't want to play you.

Play anybody, anytime. Learning how to win is also an important lesson.

I have to disagree with some good players here: playing lower rated players will not improve your chess much, if at all. Though this may not be the case for everyone, whenever I play someone significantly lower rated (in person I mean; online, I tend to be more attentive), I often end up in a (theoretically) losing position straight out of the opening because I underestimated my opponent and/or blitzed all my moves. Even though I always end up winning, I have to say playing against the significantly weaker can definitely be detrimental to one's chess, especially if you start playing moves at your opponent's level.

It actually decreases one's ability. If two people of different skill play really many games, the weaker will improve, and the stronger will degrade.

I could see that might be the case if you play most of your games with weaker players. Though, I would think that if you are consistently playing the board, and not the player, the stronger player should still be able to improve. I don't think the improvement would be massive, but I still think you could pinpoint weaknesses in your play, even by playing weaker players.

The caveat would be that you should also play plenty of stronger players and in all cases analyze your games, with an eye towards looking for weaknesses in your play.

You should always play against stronger opponents if you can. Im not saying a beginner should start playing against GMs. You should have a chance to win but it should be a real challenge. And most important is to think for yourself. Never assume your opponent is right just because he got a higher rating!