q - Personal.psu.edu - Penn State University
... football and baseball coach, webmaster for four different organizations, Sunday School teacher, … ...
... football and baseball coach, webmaster for four different organizations, Sunday School teacher, … ...
Chapter 6 Sequences and Series of Real Numbers
... {an } is monotonically increasing we have that for all n > N an ≥ aN and hence for all n > N it follows that u − ² < an ≤ u. Thus, |an − u| < ² for all n > N . Thus, lim an = u = lub S. The proof for bounded monotonically decreasing sequences is the same with the greatest lower bound playing the rol ...
... {an } is monotonically increasing we have that for all n > N an ≥ aN and hence for all n > N it follows that u − ² < an ≤ u. Thus, |an − u| < ² for all n > N . Thus, lim an = u = lub S. The proof for bounded monotonically decreasing sequences is the same with the greatest lower bound playing the rol ...
Introduction to Logic
... other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only lies at its origin, ca. 500 BC, but has been the main force motivating its development since that time until the last century. There was a medieval tradition according to which the Greek philos ...
... other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only lies at its origin, ca. 500 BC, but has been the main force motivating its development since that time until the last century. There was a medieval tradition according to which the Greek philos ...
