Exercise is a body activity that enhances or maintains physical fitness and overall health and wellness. It is performed for various reasons, including weight loss or maintenance, to aid growth and improve strength, develop muscles and the cardiovascular system, hone athletic skills, improve health, or simply for enjoyment. Many individuals choose to exercise outdoors where they can congregate in groups, socialize, and improve well-being as well as mental health.
Aerobic exercise (also known as endurance activities, cardio or cardio-respiratory exercise) is physical exercise of low to high intensity that depends primarily on the aerobic energy-generating process. "Aerobic" is defined as "relating to, involving, or requiring oxygen", and refers to the use of oxygen to meet energy demands during exercise via aerobic metabolism adequately. Aerobic exercise is performed by repeating sequences of light-to-moderate intensity activities for extended periods of time.
In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or . When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges.
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .
In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series . If the limit of the summand is undefined or nonzero, that is , then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test.
