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Exercise 1. The following lemma is important for the base case of the induction proof of the main theorem. Prove all three claims of this lemma using Proposition 2. Lemma 7. The empty set Ø can be counted by 0. The empty set is the only set that can be counted by 0 (in other words, if a set S is counted by 0, it is empty). Furthermore, the empty set cannot be counted by n > 0.

Exercise 1. The following lemma is important for the base case of the induction proof of the main theorem. Prove all three claims of this lemma using Proposition 2. Lemma 7. The empty set Ø can be counted by 0. The empty set is the only set that can be counted by 0 (in other words, if a set S is counted by 0, it is empty). Furthermore, the empty set cannot be counted by n > 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Exercise 1. The following lemma is important for the base case of the induction proof of the main theorem. Prove all three claims of this lemma using Proposition 2. Lemma 7. The empty set Ø can be counted by 0. The empty set is the only set that can be counted by 0 (in other words, if a set S is counted by 0, it is empty). Furthermore, the empty set cannot be counted by n > 0.
Transcribed Image Text:Exercise 1. The following lemma is important for the base case of the induction proof of the main theorem. Prove all three claims of this lemma using Proposition 2. Lemma 7. The empty set Ø can be counted by 0. The empty set is the only set that can be counted by 0 (in other words, if a set S is counted by 0, it is empty). Furthermore, the empty set cannot be counted by n > 0.
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