Write-Up 2: Clock Arithmetic ESSAY

Please write up your solution to Clock Arithmetic. A write-up is a detailed solution to an assigned exploration. These write-ups should be readable independently of any worksheet on which they are based, in good English, in paragraph form, and either legibly handwritten in ink or word-processed.

The paper should address the following components:

• A complete definition of the operation on the set in words.
• A complete definition of the operation on the set as a formula.
• An example of how the formula is applied to calculate the new time for each clock-addition scenario
• A complete definition of the operation on the set as an operations table.
• An example of how the table is applied to calculate the new time for each clock-addition scenario.
• A definition of closure, and a proof (generalized using the formula) or counterexample of the closure of the operation.
• A definition of commutativity, and a proof (generalized using the formula) or counterexample of the commutativity of the operation.
• A definition of associativity, and a proof (generalized using the formula) or counterexample of the associativity of the operation.
• A definition of identity, and a proof (generalized using the formula) or counterexample of the identity of the operation.
• A definition of inverses, and an explanation of whether they apply to the operation. If they apply, all inverses should be provided and justified.

Reviewing the "Tips for Write-ups" document in the Getting Started Module can help you prepare for writing this type of paper. The following checklist is adapted from this document. Does your paper...

1. communicate to the reader what the activity was about and what was the problem to be solved?
2. state your answer in a complete sentence which stands on its own?
3. provide a paragraph that discusses how the group (or you) approached the problem?
4. define variables used (if they are used) and terminology that the reader might not understand?
5. state any assumptions you made (if applicable)?
6. clearly label any pictures, diagrams, or other visual represenations?
7. give a precise and well-organized explanation of how your solution was found?
8. give acknowledgment where it is due?
9. use correct spelling, grammar, and punctuation?
10. make sure any "math" is done correctly?
11. answer the question that was originally asked?