Exercise 1.B.4

The empty set is not a vector space. The empty set fails to satisfy only one of the requirements listed in 1.19. Which one?

Answers

Since the empty set doesn’t have elements, any statement with ∀ ⁡ will be vacuously true. The only statement that doesn’t look like that is the additive identity, which we can confirm is not true because 0∉∅.

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2022-09-10 20:18
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