It is believed that high repetitions (more than 12) build muscle endurance and not strength, but to me this doesn't sound right, here's why, let's suppose for example that Ii can curl 20 pounds for 5 reps, then Ii choose to progress by increasing my reps instead of weight, therefore after some time Ii could curl 20 pounds for, say, 15 reps. This means that i turned my 5 rep max into my 15 rep max, so now my current 5 rep max had definitely increased, hence Ii built strength by using high reps. What's wrong with this reasoning? Is it the case that high reps build strength as well as low ones?