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Computer & Technology Basics Course for Absolute Beginners
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Learn basic computer and technology skills. This course is for people new to working with computers or people that want to fill in some gaps about their computer knowledge. ️ This course was developed by GCF Global. Check out their YouTube channel: https://www.youtube.com/c/GcflearnfreeOrgplus 🔗 GCF Global offers more free learning ...
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Pigeonhole Principle Examples
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SOLVED:An alternative proof of Theorem 3 based on the generalized pigeonhole principle is outlined in this exercise. The notation used is the same as that used in the proof in the text. a) Assume that ik ≤n for k=1,2, …, n^2 1 . Use the generalized pigeonhole principle to show that there are n 1 terms ak1, ak2, …, akn 1 with ik1=ik2=⋯= ikn 1, where 1 ≤k1akj 1 for j=1,2, …, n .[Hint: Assume that  akj  ikj 1, which is a contradiction. ] c) Use parts (a) and (b) to show that if there is no increasi
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