The document discusses the benefits of physical exercise on cognitive function in older adults and patients with Alzheimer's disease or mild cognitive impairment. It provides evidence from multiple reviews and studies that both aerobic and resistance training can improve executive function and delay cognitive decline. The document also describes results from trials conducted by the author showing that regular physical exercise interventions led to sustained or improved cognitive performance and functional abilities in MCI patients and helped maintain cognitive skills longer in Alzheimer's patients compared to control groups without exercise.