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Unformatted text preview: Administration 1. Midterm regrades due today! 2. Homework due on Friday. CS70: Satish Rao: Lecture 36. I Countable I Countably infinite. I Enumeration Infinities... Discrete: distribution function. Infinities... Discrete: distribution function. Real: density functions. Infinities... Discrete: distribution function. Real: density functions. Discrete: Infinities... Discrete: distribution function. Real: density functions. Discrete: finiteness Infinities... Discrete: distribution function. Real: density functions. Discrete: finiteness ? Geometric distribution has infinite support. Infinities... Discrete: distribution function. Real: density functions. Discrete: finiteness ? Geometric distribution has infinite support. Wrote down distribution with infinite support. Infinities... Discrete: distribution function. Real: density functions. Discrete: finiteness ? Geometric distribution has infinite support. Wrote down distribution with infinite support. Integers: For any value can write down probability. Infinities... Discrete: distribution function. Real: density functions. Discrete: finiteness ? Geometric distribution has infinite support. Wrote down distribution with infinite support. Integers: For any value can write down probability. Reals: Density but not probability. How big are the reals or the integers? Infinite! How big are the reals or the integers? Infinite! Is one bigger or smaller? Same size. Same size. Same number? Same size. Same number? Make a function f : Circles Squares. Same size. Same number? Make a function f : Circles Squares. f ( red circle ) = red square Same size. Same number? Make a function f : Circles Squares. f ( red circle ) = red square f ( blue circle ) = blue square Same size. Same number? Make a function f : Circles Squares. f ( red circle ) = red square f ( blue circle ) = blue square f ( circle with black border ) = square with black border Same size. Same number? Make a function f : Circles Squares. f ( red circle ) = red square f ( blue circle ) = blue square f ( circle with black border ) = square with black border One to one. Same size. Same number? Make a function f : Circles Squares. f ( red circle ) = red square f ( blue circle ) = blue square f ( circle with black border ) = square with black border One to one. Each circle mapped to different square. Same size. Same number? Make a function f : Circles Squares. f ( red circle ) = red square f ( blue circle ) = blue square f ( circle with black border ) = square with black border One to one. Each circle mapped to different square. One to One: For all x , y D , x 6 = y = f ( x ) 6 = f ( y ) . Same size. Same number? Make a function f : Circles Squares....
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 Fall '11
 Rau

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