 This sequence does not converge to any real number in the standard real topology. However, one might redefine what it means for a sequence to converge in response to this. For example, we could define convergence in terms of the arithmetic mean. Given a sequence \(x_n\), the Cesàro mean is the sequence \(C_1 = x_1\), \(C_2 = (x_1 + x_2)/2\), \(C_3 = (x_1 + x_2 + x_3)/3\), and so on. These numbers describe the average value of the sequence up to a given term. One says that a sequence \(x_n\) Cesàro converges to a number \(C\) if and only if \(C_n\) converges (in the ordinary sense) to \(C\). It is then well-known that the sequence \(0, 1, 0, 1, \ldots\) Cesàro converges to ½ (see e.g. Bashirov 2014).