Analysis: Chapter 4 Real numbers

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14 Terms

1
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Definition of upper and lower bounds.

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2
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Definition of bounded above, below and just bounded.

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3
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Definition of least upper bound.

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4
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Definition of supremum.

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5
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Axiom of completeness…

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6
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Definition of infimum.

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7
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Alternative characterization of supremum.

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8
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Alternative characterization of infimum.

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9
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Definition of maximum and minimum.

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10
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Three propositions around minimum and maximum.

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11
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Archimedean property…

(Archimedean property). For every real number x ∈ R there exists a natural number m ∈N such that x < m.

12
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Definition of a ceiling function.

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13
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Proposition & properties of infimum and supremum.

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Definition of Bernoulli’s inequality

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