Unformatted text preview: 72 Solutions to Review Exercises 30. Assume, to the contrary, that S is countable and that its elements can be listed aI, a2, a3, . ... By moving this element to the start of the list, if necessary, we may assume that al = 0.01000 .... Now the same argument as in Exercise 29 yields the result. (Note that the choice of al guarantees that b", 0.) 31. The Fields Medal is the highest honour which can be bestowed upon a mathematician, there being no Nobel Prize in mathematics. John Charles Fields (18631932) was born in Hamilton, Ontario, obtained a PhD from John Hopkins University in 1887 and served for over thirty years on the faculty of the University of Toronto. His will established the Fields Medal (under the name "International Medal for Outstanding Discoveries in Mathematics"), which was officially adopted at the International Congress of Mathematicians in Ziirich in 1932. One of the three Canadian mathematics institutes is also named after Fields. Michael Monastyrsky wrote an informative article on the history of the Fields Medal for after Fields....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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