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chapter_0/0_2/0_2_8_reading_questions.md

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+1.
+
+Q: Think back to the domino problem, at the beginning of this section. We asked
+how many dominoes are in a double-six domino _set_. Is this really a set, in our
+mathematical sense? What discrete structure would you use to represent each
+domino individually?
+
+A: No, the domino set is _not_ a set, because the order of the number matters so
+you don't repeat any pair. Thusly a sequence, or tuple, would be more
+appropriate to represent each domino individually.
+
+2.
+
+Q: A double-zero domino set would contain only one domino (both sides showing
+0). A double-one set would contain this plus the dominoes (1, 0) and (1, 1). We
+can continue in this way, creating a sequence of domino sets. Find the next
+three terms of this sequence.
+
+1, 3, _, _, _ ...
+
+A: 1, 3, 6, 10, 15
+
+The reason for this is we are summing up all the dominos, you can count starting
+like we wrote out in our investigation:
+
+(0, 6), (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6)
+
+(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 5)
+
+(0, 4), (1, 4), (2, 4), (3, 4), (4, 4) = 5 tuples
+
+(0, 3), (1, 3), (2, 3), (3, 3) = 4 tuples
+
+(0, 2), (1, 2), (2, 2) = 3 tuples
+
+(0, 1), (1, 1) = 2 tuples
+
+(0, 0) = 1 tuples
+
+1, (1 + 2), (1 + 2 + 3), (1 + 2 + 3 + 4), (1 + 2 + 3 + 4 + 5)
+
+3.
+
+Q: What questions do you have after reading this section? Write at least one
+question about the content of this section that you are curious about.
+
+A: The author makes not of graphs with edges and vertices that are related by
+some function. In the example given, there are graphs where edges are made based
+off of summing up to 7, or in the other, based off those same sets are connected
+by edges based off of if their sum is even. I don't really have a question, but
+the logic based off of these relationships are established. In other words, how
+the cardinality is established and why.

chapter_0/0_2/investigate_0.md

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+2.0:
+
+Q: A double-six domino set consists of tiles containing paris of numbers, each
+from 0 to 6. How many tiles are in a double-six domino set? How many dominoes
+are in a double-nine domino set? How many dominoes are in a double-$n$ domino
+set?
+
+This is a combinatorics problem. It is a summation.
+
+ON a double-six domino set, we can think of each domino being like a bunch of
+tuples:
+
+(0, 6), (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6)
+
+(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 5)
+
+(0, 4), (1, 4), (2, 4), (3, 4), (4, 4)
+
+(0, 3), (1, 3), (2, 3), (3, 3)
+
+(0, 2), (1, 2), (2, 2)
+
+(0, 1), (1, 1)
+
+(0, 0)
+
+A: The author makes not of graphs with edges and vertices that are related by
+some function. In the example given, there are graphs where edges are made based
+off of summing up to 7, or in the other, based off those same sets are connected
+by edges based off of if their sum is even. I don't really have a question, but
+the logic based off of these relationships are established. In other words, how
+the cardinality is established and why.
+
+And on a double-nine:
+
+(0, 9), (1, 9), (2, 9)