What did I find difficult?
Congruence Modulo n. a is said to be congruent to b modulo n, written a = b (mod n) if n | (a-b).
Division Algorithm.
This was a difficult chapter to understand. Congruence Modulo n. I understand the attributes of equivalence relations pretty well, but it is difficult for me to see how these congruence modulo n's work with reflexive, symmetric, transitive. Reading through the example seems simple to me, but I'm not sure how I would be able to do this on my own. I do look forward to trying this though.
I am also confused in how we should go about defining the distinct equivalence classes. I realize this is from a few chapters back but I am confused at how this is to work with congruence modulos. I guess the only way to learn is by doing.
What did I find interesting?
I find it interesting reading through these proofs, especially since they are congruence modulos. I am still getting to know these congruence modulos, understanding what they're about and how their equivalence classes can be proved. Walking through these step by step seems to make sense. I only wonder how I am going to deal when the homework comes around. I think I find this congruence proofs with equivalence classes interesting because it's a new concept. I hope to learn more about it and that it can teach me how to think. I hope to see that this is important in programming - I feel that so much of programming is math.
Congruence Modulo n. a is said to be congruent to b modulo n, written a = b (mod n) if n | (a-b).
Division Algorithm.
This was a difficult chapter to understand. Congruence Modulo n. I understand the attributes of equivalence relations pretty well, but it is difficult for me to see how these congruence modulo n's work with reflexive, symmetric, transitive. Reading through the example seems simple to me, but I'm not sure how I would be able to do this on my own. I do look forward to trying this though.
I am also confused in how we should go about defining the distinct equivalence classes. I realize this is from a few chapters back but I am confused at how this is to work with congruence modulos. I guess the only way to learn is by doing.
What did I find interesting?
I find it interesting reading through these proofs, especially since they are congruence modulos. I am still getting to know these congruence modulos, understanding what they're about and how their equivalence classes can be proved. Walking through these step by step seems to make sense. I only wonder how I am going to deal when the homework comes around. I think I find this congruence proofs with equivalence classes interesting because it's a new concept. I hope to learn more about it and that it can teach me how to think. I hope to see that this is important in programming - I feel that so much of programming is math.
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