Partition of Integers with mod

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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?
 

Answers and Replies

  • #2
Dick
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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?

I'm not too clear on what your argument is supposed to mean. What's R? But -5=3 mod 4 since (-5)=(-2)*4+3. Hmm, I think I see. R means 'remainder', yes?
 
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Sorry, I forgot to mention this is far from a formal proof. R just means remainder.
 
  • #4
Dick
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Sorry, I forgot to mention this is far from a formal proof. R just means remainder.

Yeah, it is far from formal. But I see what you are doing. Are you supposed to give something formal or just answer yes or no?
 
  • #5
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Just answer yes or no. And, you answered my question. I'm pretty sure the answer is yes. Thanks.
 

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