18.100B.Homework1

# 18.100B.Homework1 - 18.100B/C: Fall 2008 Homework 1...

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18.100B/C: Fall 2008 Homework 1 Available Monday, September 8 Due Wednesday, September 17 Problems 1–4 cover material discussed in the ﬁrst week of classes, while problems 5–9 cover material from the second week. Turn in the homework by 11am on Wednesday, September 17, in 2-108. For 18.100B it should be put in the bin corresponding to the lecture you regularly attend (regardless of which one you may be ofﬁcially enrolled in). If you are enrolled in 18.100C put your homework in the C bin in any case. 1. Suppose that S is a set and ± is a relation on S with the following properties: For all x S , x ± x . For all x, y S , if x ± y and y ± x then x = y . For all x, y, z S , if x ± y and y ± z , then x ± z . Deﬁne a new relation on S by x y iff x ± y and x ² = y . Does this deﬁne an order conforming to Deﬁnition 1.5 in Rudin? If so, prove it; if not, exhibit a counterexample. 2. (a)

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## This note was uploaded on 12/07/2011 for the course MATH 18.100B taught by Professor Prof.katrinwehrheim during the Fall '10 term at MIT.

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18.100B.Homework1 - 18.100B/C: Fall 2008 Homework 1...

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