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We Lie to Students

Mathematical Lies and the Lying Liars who Teach Them — or — The Peano Postulates have been Drinking, Not Me. We Lie to Students. . Precalculus : A Good Time to Stop Lying. Key Ideas. Closure Identity elements Inverse elements. Back to the Beginning: Counting. Peano Postulates.

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We Lie to Students

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  1. Mathematical Lies and the Lying Liars who Teach Them— or —The Peano Postulates have been Drinking, Not Me

  2. We Lie to Students

  3. Precalculus: A Good Time to Stop Lying

  4. Key Ideas • Closure • Identity elements • Inverse elements

  5. Back to the Beginning: Counting

  6. Peano Postulates • 0 ∈ℕ • n∈ℕ ⇒ n + 1 ∈ℕ

  7. Peano Postulates • 0 ∈ℕ • n∈ℕ ⇒ n + 1 ∈ℕ • n + 1 = 0 ⇒ n∉ℕ • n + 1 = m + 1 ⇒ n = m

  8. Peano Postulates • 0 ∈ℕ • n∈ℕ ⇒ n + 1 ∈ℕ • n + 1 = 0 ⇒ n∉ℕ • n + 1 = m + 1 ⇒ n = m • 0 ∈S and ∀n∈S, n + 1∈S⇒ S = ℕ

  9. Geometric Construction

  10. Geometric Construction

  11. The Natural Numbers ℕ (It’s a lot easier to find an image for “converse” than “inverse”)

  12. Natural Numbers and their Opposites ℤ = ℕ∪–ℕ

  13. The Integers ℤ

  14. Ratios of Integers ℚ = {a/b with a,b∈ℤ and b ≠ 0}

  15. The Rational Numbers

  16. Sequences of Rational Numbers

  17. The Real Numbers

  18. Square Roots of Negative Numbers Comic by Xkcd, http://xkcd.com/179/

  19. The Complex Numbers

  20. We’re Still Lying

  21. Time’s Up! • Apologies to Al Franken and Tom Waits for the titles. • Isaac Greenspan • isaac@isaacgreenspan.com • teacher, editor, writer, consultant • http://talks.isaacgreenspan.com/MMCIgnite2012.pdf

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