L10_filled - Day 10 Ahhhhhh Real Numbers 2 Todays Travel...

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1 Day 10 Ahhhhhh… Real Numbers 2 Today’s Travel Plans An Excursion into Geometry …Then Why… Irrational Numbers Real Numbers Getting a Grip on Root 2 The Babylonian Method The Unholy Real Numbers
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2 3 So Last Time We Learned That… The Base 10 expansion of an integer can be extend to fractions allowing one to write any fraction as a decimal number . Every fraction‘s decimal form can be found via _______ ________. A completely reduced fraction is represented by a ____________ decimal if and only if its denominator is a divisor of a power of 10 A completely reduced fraction is represented by a ____________ decimal if and only if it can be rewritten as a sequence of digits over a sequence of _______. As a consequence we have that 1.00000 … = 1. 0 g = 1 = 9 9 = 0. 9 g = 0.99999 … 4 A discursion into Geometry We’ll now take a short adventure into geometry. Imagine three line, one moving strait across, one moving strait up, and one at a diagonal… like this. At the top of the picture, you’ll see the sun. It’s beaming down light [imagine]. To the right there is a search light looking out for an adorable escaped monkey.
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3 5 A discursion into Geometry II Compare the two images of the monkey climbing along the brown “tree like” line. What else is different in the two pictures besides the monkey’s location. 6 A discursion into Geometry III Is anything different from the last slide in these two cases? What’s happening when the monkey climbs along the vertical line?
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7 A discursion into Geometry VI What’s happening when the monkey moves along the ground? 8 A discursion into Geometry V The ___________ of the monkey is a literal example of what is called a mathematical _____________. Compare with a movie theater or the overhead… When two _______________ lines are joined end-to-end, changing position on one line does not change the relative position on the other line. Said Another way, two lines are ________________ if one can move the ___________ on one line, with out moving the ___________ on the other. Such Lines are important because they form the sides of the
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This note was uploaded on 07/23/2011 for the course MGF 1107 taught by Professor Staff during the Fall '08 term at University of Florida.

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L10_filled - Day 10 Ahhhhhh Real Numbers 2 Todays Travel...

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