The discussion revolves around whether specific subsets of integers form a partition of the set of integers, particularly focusing on integers divisible by 4 and those equivalent to 1, 2, or 3 mod 4.
Some participants express confidence in the partitioning argument, while others seek clarification on terminology and the need for formal proof. There is a mix of informal reasoning and attempts to understand the requirements for a formal proof.
Participants note that the discussion is not intended to be a formal proof and question whether a simple affirmative or negative response suffices for the homework requirement.
nicnicman said:Homework Statement
Are the following subsets partitions of the set of integers?
The set of integers divisible by 4, the set of integers equivalent to 1 mod 4, 2 mod 4, and 3 mod 4.Homework Equations
The Attempt at a Solution
Yes, it is a partition of the set of integers. Consider 4/4 = 1, 5/4 = 1 R 1, 6/4 = 1 R 2, 7/4 = 1 R 3.
However, how would you create a negative number like -5?
nicnicman said:Sorry, I forgot to mention this is far from a formal proof. R just means remainder.