Final answer:
The pathological presence of erythrocytes in the urine is called hematuria, which can occur due to nephritis, trauma, or kidney stones, among other causes.
Step-by-step explanation:
The pathological presence of erythrocytes in the urine is called hematuria. This condition can be caused by various diseases and conditions such as nephritis, trauma, tuberculosis of the kidney, and kidney stones. On microscopic examination of urine, the presence of both red blood cells (RBC) and white blood cells (WBC) can indicate hematuria. Hematuria should be distinguished from hemoglobinuria, which involves the presence of hemoglobin without intact red blood cells and can be observed in conditions like malaria and typhoid.