An Introduction To Mathematical Analysis Exam 2026 Questions and Answers

An Introduction To Mathematical
Analysis Exam 2026 Questions and
Answers

Axiom of Completeness - Correct answer-Every nonempty set of real numbers that

is bounded above has a least upper bound.

upper bound - Correct answer-a number equal to or greater than any other number

in a given set

Least upper bound - Correct answer-if x is an upper bound and there does not exist

a y smaller than that is also an upper bound

Greatest Lower Bound - Correct answer-if x is a lower bound and in the set then it

is a greatest lower bound

Bounded - Correct answer-A set is bounded if it contains both a lower and upper

bound

Maximum - Correct answer-The largest member in the set.

infemum - Correct answer-greatest lower bound


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, principle of induction - Correct answer-Let P be a sub set of Z if 1 exists in p and if

n exists in p implys n+1 exists in p then p=Z

Denseness of irrationals in reals - Correct answer-For All a,b e R such that there

exists r e Q such that a<r<b

Russels Paradox - Correct answer-Is a set an element of a set

Union - Correct answer-A U B= {x|x e A or x e B}

Function - Correct answer-if f is a subset of AxB if for every point x e A there

exists 1 y e B such that (x,y) e f then f is a function

Range - Correct answer-F[A]= {f(x)|x e A}

One to one - Correct answer-f:A->B is 1 to 1 if for all a1,a2 e A such that a1≠a2 we

have f(a1)≠f(a2)

one to one correspondence - Correct answer-A maps into and onto B

Composition of functions - Correct answer-

relation - Correct answer-a relation is a subset of AxB

reflexive relation - Correct answer-∀x ∈ X : x R x.

symmetric relation - Correct answer-a relation on set A is symetric if aRb a=bRa




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