Mathematics 301-002 Fall 2017 The computer scientists Richard Conway and David G
ID: 3148803 • Letter: M
Question
Mathematics 301-002 Fall 2017 The computer scientists Richard Conway and David Gries once wrote: The absence of error messages during translation of a computer program is only a necessary and not a sufficient condition for reasonable program correctness. Rewrite this sentence without using the words necessary or sufficient. 4. A well-known theorem in Hilbert Space Operator Theory is this one: Theorem. All subnormal operators are intransitive. Note that you do not need to know the definitions of the words involved. However it will be helpful to point out that (1) "intransitive" means "not transitive"; and (2) not every operator is subnormal. Dean Olin of the College of Arts and Sciences is a mathematician who published a number of papers on this very subject, although the result quoted above was first proved by Scott Brown. Which of the following might be a plausible beginning for a proof of this The- orem, using a proof by contradiction? (a) Let T be a subnormal operator. We will prove that T is intransitive. (b) Let T be an operator. We will show that, if T is not subnormal, then 1 is transitive. (c) Let T be a subnormal operator and sunn derive a statementExplanation / Answer
If there is only absence of error messages during translation of a computer program, then it is not a condition for reasonable [program] correctness.