Flashcards
§0 Preliminaries
Cards in this deck (5)
- 1Upper boundAn \(\underline {upper-bound}\) of a subset D of ℝ is any c ∈ ℝ s.t. ∀ d ∈ D,
d ≤ c. - 2Bounded aboveWe say D is \(\underline {bounded-above} \) if it has an upper bound.
- 3Least upper boundA \(\underline {least-upper-bound} \) of D is an upper bound of D that is \(\underline {less-then} \) any other upper bound of D, so is the smallest bound. Thus c is a least upper bound of D iff:
(i) c is an upper bound of D; and
(ii) if c' is any upper bound of D, then c ≤ c' - 4Order-CompletenessThe \(\underline {order-completeness} \) property of ℝ states that:
every non-empty subset of ℝ that is bounded above must have a least upper bound. - 5Order-DensityThe order density of ℚ in ℝ states that between any 2 distinct real numbers there is a rational.
i.e. if a,b ∈ ℝ and a < b, then ∃ q ∈ ℚ s.t. a < q < b
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- Diploma/Certificado de qualificação profissional de nivel 3 Mathematics (Topology (MATH313)) Flashcards on §0 Preliminaries , created by Amy Wogan on 27/04/2016.
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