Lemma 2.3.7. Let T be a collection of sets with the property that the intersec- tion of any two members of T is in T. If {U1,..., Un} is a finite subcollection of sets from T, then the intersection N- Ui is in T. =D1

Lemma 2.3.7. Let T be a collection of sets with the property that the intersec- tion of any two members of T is in T. If {U1,..., Un} is a finite subcollection of sets from T, then the intersection N- Ui is in T. =D1

Name: The method of proof is induction since the set of natural numbers is t
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Description: The method of proof is induction since the set of natural numbers is the replacement set but I don’t know how to set this up **Lemma 2.3.7**: Let $ \mathcal{T} $ be a collection of sets with the property that the intersection of any two members of

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The method of proof is induction since the set of natural numbers is the replacement set but I don’t know how to set this up

**Lemma 2.3.7**: Let $ \mathcal{T} $ be a collection of sets with the property that the intersection of any two members of $ \mathcal{T} $ is in $ \mathcal{T} $. If $ \{U_1, \ldots, U_n\} $ is a finite subcollection of sets from $ \mathcal{T} $, then the intersection $ \bigcap_{i=1}^n U_i $ is in $ \mathcal{T} $.

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