13.4. Addition Modulo k

Try these first

1. 1.

   What is a group in abstract algebra?

   Hint

   Think about the properties that define a group.

2. 2.

   Identify the identity element for addition in integers.

   Hint

   Consider what number you can add without changing the value.

3. 3.

   What is the requirement for a set to be a group?

   • It must have closure.
   • It must require subtraction.
   • It must include fractions.

   Hint

   Reflect on what properties are essential for forming a group.

4. 4.

   True or False: Addition modulo k is not a valid group operation.

   • True
   • False

   Hint

   Look back to how addition modulo k is defined.

5. 5.

   Create a new example set and operation, showing if it satisfies the four properties of groups.

   Hint

   Use the defined properties for each check.

6. 6.

   Discuss how arching inverses work in negative and positive integers under addition.

   Hint

   Think about how inverses are defined relative to the identity.