Year 1 Analysis Flashcards

1
Q

Statement, truth tables,

A

e

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2
Q

distributive, de morgan

A

e

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3
Q

def function

A

e

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4
Q

field axioms

A

e

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5
Q

field axoim results

A

e

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6
Q

order axioms

A

e

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7
Q

order results

A

e

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8
Q

def supremum

A

e

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9
Q

max s = sup sresult

A

e

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10
Q

completeness axiom

A

e

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11
Q

archimidean postulate

A

e

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12
Q

triangle inequality

A

e

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13
Q

binomial inequality

A

e

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14
Q

convergence

A

e

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15
Q

1/n

A

e

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16
Q

simple convergence resaults

A

e

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17
Q

L<M convergence proof

A

e

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18
Q

uniqueness of limits proof

A

e

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19
Q

convergent sequence is bounded proof

A

e

20
Q

algebra of limits

A

e

21
Q

mod convergence results

A

e

22
Q

def diverges

A

e

23
Q

monotone def

A

e

24
Q

monotone and bounded above converges proof

A

e

25
Q

root 2 show

A

e

26
Q

sandwich theorem

A

e

27
Q

bitten sandwich theorem

A

e

28
Q

1/an diverges proof

A

e

29
Q

lemma an+1/an

A

e

30
Q

Growth factor test

A

e

31
Q

subsequence def

A

e

32
Q

any subsequence converges

A

e

33
Q

Bolzano weirstrass proof

A

e

34
Q

def series

A

e

35
Q

if series converges proof

A

e

36
Q

AOL for series

A

e

37
Q

a series less than another

A

e

38
Q

two results non negative terms

A

e

39
Q

absolute convergence defq

A

e

40
Q

if absolute then normal

A

e

41
Q

rearrangement of series

A

e

42
Q

Comparison test

A

e

43
Q

A’alemberts ratio test

A

e

44
Q

Leibniz alternating series test

A

e

45
Q
A