Theorems Y1S1 Flashcards by 0a548ck Kan3

Q

What are the axioms for real numbers?

A

Field axioms
Completeness axioms

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Q

Random numbered theorem about bounded sets

A

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Q

Archimedean Postulate

A

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Q

Triangle inequality

A

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Q

Reverse Triangle inequality

A

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Q

Bernoulli’s inequality

A

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Q

Uniqueness of limits

A

For real or complex sequences there can only be 1 limit

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Q

Random theorem in start of limits

A

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Q

Algebra of limits

A

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Q

Convergence test 1

A

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Q

Squeeze theorem

A

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Q

Bitten squeeze theorem

A

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Q

Growth factor test

A

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Q

Bolzano-weierstrass

A

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Q

Cauchy convergence

A

A sequence converge iff it is a cauchy sequence

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Q

Algebra of limits for series

A

Q

Simple inequalities with sequence

A

Q

Convergence by absolute convergence

A

Q

Rearrangement of series

A

Q

Comparison test

A

Q

D’Albert’s ratio test

A

Q

Cauchy condensation test

A

Q

Leibniz alternating series test

A

Q

Cauchy product of series

A

Q

Nested interval thoery

A

Q

An uncountable region

A

Q

Convergence with sup and inf

A

Q

Intermediate value theorem

A