Math 23bHomework 7Spring, 2009Due Wednesday, April 8.Be sure to write clearly, using complete sentences. Do not use abbreviations like s.t., w/,w/o, b/c, c/o, etc. In all problems you must prove that your answer is correct, even if theproblem does not explicitly ask you to do so. In addition, one third of the grade on eachexercise will be determined by the presentation of your argument.Even if your answeris in the end correct, you will lose points if there are irrelevant, extraneous or incorrectstatements in your argument. There will be no revision for this homework. Since thereis restriction on how much you can write in each problem, you should consider carefullywhat is essential to include, before writing your final answers.1. Lety > x.(a) In 1 line, prove that there is a positive integernsuch thatn(y-x)>1.(Use theArchimedean property.)(b) In no more than 10 lines, prove that there is an integermsuch thatm > nx≥m-1.(Consider the casenx >0 andnx≤0 separately. Use the Archimedean property to findonem, and then use the Well Ordering property to find the smallest
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