October 20

• Homework: pentahedron; origami?
• If $x^3=26$ and $y^2=9$, what is bigger, $x$ or $y$? 
• Two players try to move short hand to 5 o'clock. They start at 1, and can move it ahead 2 or 3 hours. Who wins?
• Geometric progressions - how to find their sums.  When the sum converges. 
• What about other convergences: example of $1+1/2+1/3+\ldots$
• $a^6\mod 7$ for $a=1,2,\ldots,6$.
• The following sets are given: $$A = \{1, 3, 7, 137\}, B = \{3, 7, 100\}, C = \{0, 1, 3, 100\}, D = \{0, 7, 100, 333\}.$$
  Describe the sets:
• $A \cup B$;
• $A\cap B$;
• $(A \cap B)\cup D$;
• $C \cap (D\cap B)$;
• $(A\cup B)\cap (C \cup D)$;
• $(A\cap B)\cup (C \cap D)$;
• $(D\cup A)\cap (C \cup B)$;
• $(A\cap (B\cap C))\cap D$;
• $(A\cup (B\cap C))\cap D$;
• $(C \cap A)\cup ((A\cup (C \cap D))\cap B)$