Counterexample36

An example explains the impotance of assumption in L’Hospital’s Rule
Solution to Elementary Analysis: The Theory of Calculus Second Edition Section 30 Exercises 30.6 Sol...
Find limits of sequences III
Solution to Elementary Analysis: The Theory of Calculus Second Edition Section 7 Exercise 7.5 We sha...
Sequence of rational numbers has an irrational limit
Solution to Elementary Analysis: The Theory of Calculus Second Edition Section 7 Exercise 7.4 Soluti...
Not every ideal is prime
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.34 Solution:...
Prove that a given quotient ring is not an integral domain
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.17 Solution:...
Not all ideals are prime
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.9 Solution: ...
The quaternion group is not a subgroup of Symmetric group for any n less than 8
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.7 Solution: ...
The direct product of groups with no nonnormal subgroups may have nonnormal subgroups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.5 Solution: ...
In a noncommutative ring, the set of nilpotent elements need not be an ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.31 Solution:...
The intersection of an ideal and a subring is a subideal, but not necessarily vice versa
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.20 Solution:...