# E–pub [ Proof and the Art of Mathematics] Par Joel David Hamkins

## Joel David Hamkins á 5 characters

D severe errors early in the book I even e mailedthe author and have eceived no eplyDear SirOn page 3 youauthor and have eceived no eplyDear SirOn page 3 you the natural numbers as 0 1 2 3 In doing so by distinguishing natural number from 1 2 3 a definition which is common in many mathematical texts especially undergraduate textbooks in elementary number theory In addition you also explain that subtraction between two natural

__"numbers does not always esult in another natural number and use this as a justification for the integers Of course "__does not always esult in another natural number and use this as a justification for the integers Of course could define subtraction in the natural numbers as cut off subtraction which would allow subtraction "between any two natural numbers however you make no mention of "any two natural numbers however you make no mention of mathematical operation in the text On page 10 you give Theorem 6 For any natural number n the number n2 n is even Clearly this is true and defined in the natural numbers as n2 is always eual or greater than nThe problem is in proof 2 by High A leading esearch mathematician presents a series of engaging and compelling mathematical statements with interesting elementary proofs These proofs capture a wide ange of topics including number the. Great book I ecommend it for anyone who is interested in math Whether you are a beginner or advanced "you will surely find something in the book that catches your attention The author of "will surely find something in the book that catches your attention The author of book is a world class set theorist who probably than anyone else has promoted a multiverse ealism in set theory This argument somewhat crudely advances the point that the independence esults obtained from the method of forcing suggest a multiplicity of set theory universes similar to that of non Euclidian geometries In addition he has also advanced the idea that the phenomenon of independence can even be found at the level of arithmetic I think he is wrong and my particular philosophical inch is better satisfied by the work of Hugh Woodin However the point emains that Joel David Hamkins is an exceptional philosophically astute mathematician whose work I have enjoyed immensely So I was disappointed when I discovere. An introduction to writing proofs presented through compelling mathematical statements with interesting elementary proofsThis book offers an introduction to the art and craft of proof writing The author. ,

Chool algebra in which you prove this

__"Theorem By Rewriting N2 N Nn "__by ewriting n2 n as nn n 1 is not a natural number take n0 as your previous comments on page 3 point out uite naturally some may consider this a minor uibble however as the text has made the definitions of natural number and subtraction although informal at least conceptually clear The proof as it stands fails in the natural numbersThis does not seem to be a misprint and this is my point as he "Makes A Similar Mistake "a similar mistake page 12 In short very disappointed and so cannot ecommend the book I will not continue with the book and will be Letters to Rollins returning my copy Excellent purchase especially like the mathematical habits sections which will surely cause a moment ofeflection and will serve as conversation starters The author demonstrates his ability to write proofs and his inability to explain how to write them I cannot believe that anyone would find this helpfu. Ory combinatorics graph theory the theory of games geometry infinity order theory and Britain, Europe And The Third World real analysis The goal is to show students and aspiring mathematicians how to write proofs with elegance and precisi.

Joel David Hamkins