Lamport how to write a proof sequence

Lamport makes proofs easier to understand by the introduction of rigour in structure and in naming: structure to formally identify the roles of statements and how they connect together; naming to make it clear which facts are being used and refered to.

Proof writing class

He says that once you have a hierarchical proof, you can use pieces of it in new proofs very easily. Lamport makes proofs easier to understand by the introduction of rigour in structure and in naming: structure to formally identify the roles of statements and how they connect together; naming to make it clear which facts are being used and refered to. So, how should one begin? And an author can post the hierarchical proof on his or her website, perhaps using hypertext to allow readers to hide or show the details in each step or to include summaries of the main ideas in each step of the proof. Share this:. The talk generated a lot of questions, and I heard conference attendees chatting about it all day. A missing hypothesis, such as that a set must be nonempty, which is a trivial omission in a mathematical theorem, can mean a serious bug in an algorithm. Some of them felt very strongly that hierarchical proofs would damage the beauty of their work. Otherwise, your natural desire to confirm what you already believe to be true will cause you to miss gaps in the proof; and every gap could hide an error that makes the entire result wrong. We also need to be aware of our own psychological bias: When you write a proof, you believe the theorem to be true. I'll give you proof! Along the way, several unstated implications and pre-requisities in the original come to light and are addressed. Leslie Lamport, clad in a t-shirt that says "You want proof? It is little wonder that so few of them succeed. A working example through the paper is based on a proof from a celebrated mathematics text book Calculus by Spivak.

Proof sketches can be used at any level in a hierarchical proof, including before the highest-level proof. The best way I know to eliminate errors is to imagine that there is a curious child sitting next to us.

As I told my class, the only thing worse than the alphabet in math is not having the alphabet in math.

How to write a proof of evidence

For example, if you want to change one assumption slightly or focus on solutions that have different properties, you will be able to tell very easily which parts of the proof can stay the same and which parts will need to change. You can begin by just adding structure to an existing proof… Start by rewriting a simple proof and then try longer ones. I am a computer scientist who was educated as a mathematician. The best way I know to eliminate errors is to imagine that there is a curious child sitting next to us. This week, I am attending the Heidelberg Laureate Forum, a math and computer science analogue of the Lindau Laureate forum for Nobel Prize winners, and writing for the forum blog. Lamport makes proofs easier to understand by the introduction of rigour in structure and in naming: structure to formally identify the roles of statements and how they connect together; naming to make it clear which facts are being used and refered to. A reader not interested in the details of that part of the proof can read just the proof sketch and skip the steps and their proofs. Structured proofs were therefore an obvious solution. Proof sketches can be used at any level in a hierarchical proof, including before the highest-level proof. The talk generated a lot of questions, and I heard conference attendees chatting about it all day. These algorithms can be quite subtle and hard to get right; their correctness proofs require a degree of precision and rigor unknown to most mathematicians and many computer scientists.

This week, I am attending the Heidelberg Laureate Forum, a math and computer science analogue of the Lindau Laureate forum for Nobel Prize winners, and writing for the forum blog.

Students are expected to learn how to write logically correct proofs from examples that, when read literally, are illogical.

proof writing style

Such structuring Lamport says makes it possible to avoid errors, but hard work is still needed to make it probable! It is little wonder that so few of them succeed.

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A Computer Scientist Tells Mathematicians How To Write Proofs