PDF-2BENJAMINJOHNSONsupTistheleastupperboundforT,wehavesupTB.Thuswehavema

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2isirrationalProofbycontradictionSupposecisrationalIfcp 2isalsorationalthensincerationalnumbersareclosedundersubtractioncp 2cp 2isrationalButweveshownp 2isirrationalacontradictionContinu

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