Problem 35E

Does the check digit of an ISSN detect every error where two consecutive digits are accidentally interchanged? Justify your answer with either a proof or a counterexample.

Discrete Mathematics CS225 Terms and concepts: Week 2 Reading 145-159, 165-167. 183-184. 201-203 and Lectures and Supplemental Info List of Types of Numbers: • Natural numbers ( ℕ ): Counting numbers. {0, 1, 2, 3…} • Integers ( ℤ ): Positive and negative counting numbers. {…-2, -1, 0, 1, 2, …} • Rational numbers ( ℚ ): Numbers that can be expressed as a ratio of an integer to a non-zero integer. ◦ Quotients of integers. ◦ All integers are rational, but not all rational numbers are integers. • Real numbers ( ℝ ) : Numbers that have decimal representations. ◦ Can be positive, negative, or zero. ◦ All rational numbers are real, not all real numbers are rational. • Irrational numbers (I): Real numbers that are not rationa