I guess you should provide some context behind the usage of the notations. Because there might not be a standard notation for what the author wants to discuss, or the author very well could be using a non-standard notation.logan3 said:Maybe it's explained somewhere in her book, but what do the Hs and *s mean beside some of the problems in Epp's Discrete Math, 4E textbook?
Are there any other notations I should make note of in the book as well?
Thank-you for your help.
I do understand what context means. However, you don't understand how to be polite. So I won't further respond to your posts.skeeter said:you don't understand what context means ... in what specific concept/topic is this notation used ?
can you cite a specific chapter, preferably with a page number(s)?
logan3 said:I emailed the author. She said that the meaning of these two symbols were placed only under the first Exercise Set of each Chapter, rather than in the Preface. "Appendix B contains either full or partial solutions to all exercises with blue numbers. When the solution is not complete, the exercise number has an H next to it. A ✶ next to an exercise number signals that the exercise is more challenging than usual."
The H and * problems, also known as the Hilbert's and Post's problems, are two unsolved mathematical questions that were first proposed by mathematicians David Hilbert and Emil Post in the early 20th century. These problems have been the subject of much research and discussion in the field of mathematics, as they represent fundamental questions about the foundations of mathematics and the limits of its logical systems.
The H problem, also known as Hilbert's Entscheidungsproblem (decision problem), asks whether there exists a mechanical procedure or algorithm that can determine the truth or falsity of any mathematical statement. This problem is important because it relates to the concept of computability and the limits of what can be proven or disproven by a machine, which has implications for the field of computer science and artificial intelligence.
The * problem, also known as Post's problem or the Post correspondence problem, asks whether there exists a finite set of string rewriting rules that can generate an infinite sequence of strings. This problem is significant because it relates to the concept of undecidability and the limits of what can be computed or solved by a machine, which has implications for theoretical computer science and the study of computation.
There have been many attempts to solve the H and * problems, but so far, they remain unsolved. Several mathematicians and computer scientists have made significant contributions to these problems, including Kurt Gödel, Alan Turing, and Stephen Kleene. While some progress has been made, these problems still represent some of the most challenging and unsolved questions in mathematics and computer science.
The H and * problems are closely related, as they both deal with fundamental questions about the limits of mathematics and computation. The H problem is concerned with the limits of what can be proven or disproven by a machine, while the * problem is concerned with the limits of what can be computed or solved by a machine. Both problems have implications for our understanding of the foundations of mathematics and the capabilities of machines.