A school contains students in grades 1, 2, 3, 4, 5, and 6. Grades 2, 3, 4, 5, and 6 all contain the same number of students, but there are twice this number in grade 1. If a student is selected at random from a list of all the students in the school, what is the probability that she will be in grade 3?

Operator norm convergence

Prove (show) that operator norm convergence implies strong convergence.

Let d be a metric on X. Determine all constants k such that (i) kd,(ii) d + k is a metric on X.