Happy to help, but i just think you are confusing muscular strength with muscular endurance. Just rememeber that once you can perform an exercise for more than about 5 reps, you start training muscular endurance, not muscular strength. To increase your strength, you need to alter some aspect of the exercise to make it more challenging, thats why beginning to train one arm push ups would be the best way for you to gain strength. But if you just want to be able to do more pushups(increase your endurance), then yes, perform submaximal sets(of about 10-20, or even as little as 5 reps) constantly throughout the entire day. This takes a lot of committment, but is highly effective. This method of training is known as "greasing the groove" and was developed by Pavel Tsatsouline(a fantastic strength trainer and the guy responsible for bringing kettlebell training to amerca). The concept of greasing the groove works for just about any exercise, I am personally using it to increase my maximum number of muscle ups. Let me know if you have any more questions, also please check out my website at , I have a lot of tutorials on there that will help you out