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
©COPYRIGHT 2025, ALL RIGHTS RESERVED 1
, 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
©COPYRIGHT 2025, ALL RIGHTS RESERVED 2
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
©COPYRIGHT 2025, ALL RIGHTS RESERVED 1
, 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
©COPYRIGHT 2025, ALL RIGHTS RESERVED 2
