13.3.1. Group of Integers under Addition

Try these first

1. 1.

   What is the identity element for the group of integers under addition?

   Hint

   Think about what number does not change another number when added.

2. 2.

   State one property of a group.

   Hint

   There are multiple properties to choose from.

3. 3.

   What does the closure property imply in the context of groups?

   • The operation must be commutative.
   • The result of the operation on any two elements must be within the set.
   • There must be an identity element in the set.

   Hint

   Reflect on the examples of groups we've covered.

4. 4.

   True or False: Every element in a group has an inverse.

   • True
   • False

   Hint

   Think about the properties that define a group.

5. 5.

   If a group has elements {1, 2, 3} under addition mod 4, list all possible sums of two elements and analyze if this set forms a group.

   Hint

   Consider closure and whether each result remains in the set.

6. 6.

   Given the integers with an operation augmented by a new 'twist' where n=3 (addition mod 3), what are the group properties? List inverses.

   Hint

   Examine how mod 3 affects numbers and which results stay within our defined set.