Math for Liberal Studies

What is an identification number?  An identification number is a sequence of digits and/or numbers that identifies an object, person, place, or concept  The number should unambiguously identify something: no two things should have the same ID number

Where have you encountered ID numbers?  License plate  Driver’s license number  Student ID number  Social Security number  Phone numbers  Credit card numbers  ISBN (International Standard Book Number)  UPC (Universal Product Code)  Many, many more…

Are ID numbers random?  What happens if you go to Amazon.com and type in a random sequence of digits for a credit card number?

Security Features  How does the computer know that the number you typed in isn’t valid?  Should the computer have to look through all the millions of credit card numbers to make sure that yours isn’t on the list?

Checking Validity  Most ID numbers have a way to check to make sure that the number is valid  This is not just for security, but to detect errors  If the ID number is entered incorrectly, it is important that the error is caught

Kinds of Errors  Substitution: instead of  This error is the most common, occurring almost 80% of the time  Transposition: instead of  This error accounts for around 10% of all errors  Jump transposition: instead of  This error is much rarer, accounting for only about 1% of all errors