Yes DMS, rest is definately nessisary, or all you will be building is muscle and cardio vascular endurance. Intensity doesnt mean no rest, And it cant be measured by sweat. although sweat is a good indication that your working hard, and your heart rate is up.

To me intensity is mental, (caution, sweeping generalization about pl's) powerlifters lift with the extreme intensity, but have been known to take 4-5 minutes between sets. Intensity to me is the way you move the weights ... do you push yourself? do you move the wieght with authority? after your set do you feel like you could run through the wall? To me thats intensity, its all about mental attitude.

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I don't do this for my family, my friends, women, accolades, pride, or ego. I do it for me and no one else, its just part of who I am.