Quiz One Review

Question 1

What does it mean if a set S is bounded?

Answer 1

There exists L,U€ Reals s.t. L<=s<=U for all s€S

Question 2

What does it mean that a set S has a maximum?

Answer 2

There exists M€S such that s<=M for all s€S

Question 3

What does it mean that a set S has a minimum?

Answer 3

There exists m€S such that m<=s for all s€S

Question 4

What is an infimum of set S?

Answer 4

The greatest lower bound of S denoted inf(S)

Question 5

What is a supremum of a set S?

Answer 5

The least upper bound of S denoted sup(S)

Question 6

What is a neighborhood of x?

Answer 6

If x€Reals, then a subset (I) of the Reals is called a neighborhood if there exists €>O such that the open interval (x-€,x+€) is a subset of I

Question 7

What is a sequence?

Answer 7

A function from N (naturals) to R (reals), n to f(n)

Question 8

What does it mean that a sequence converges (by limit definition)?

Answer 8

A sequence fn converges to a real number A if for all €>0, there exists an N€naturals such that for all n€naturals, |fn-A|<€

Question 9

Are limits unique?

Answer 9

Yes, so if a sub n converges to A and b sub n converges to A, then A=B

Question 10

What’s a Cauchy sequence?

Answer 10

A sequence is Cauchy iff for all €>0 given, there exists an N€naturals such that for all m,n>=N |asubn-asubm|<€