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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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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