For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.
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Transcript of For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.
![Page 1: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/1.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
The “No WAY!” The “No WAY!” moment in moment in
mathematicsmathematics
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A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 3: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/3.jpg)
A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 4: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/4.jpg)
A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 5: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/5.jpg)
A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 6: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/6.jpg)
A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 7: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/7.jpg)
A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 8: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/8.jpg)
A Countable SetA Countable Set
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
![Page 9: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/9.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
The Diagonalization The Diagonalization ArgumentArgument
Georg Cantor
1876
![Page 10: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/10.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
The Diagonalization The Diagonalization ArgumentArgument
![Page 11: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/11.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
Georg Cantor
1874
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 13: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/13.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 14: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/14.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 15: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/15.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 16: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/16.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 17: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/17.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 18: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/18.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
![Page 19: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/19.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
Cantor’s Original ArgumentCantor’s Original Argument
L
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
![Page 23: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/23.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
![Page 24: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/24.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
![Page 25: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/25.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
![Page 26: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/26.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
...
![Page 27: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/27.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
... ...
![Page 28: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/28.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
![Page 29: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/29.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument
![Page 30: For slideshow: click “Research and Talks” from The “No WAY!” moment in mathematics.](https://reader030.fdocuments.in/reader030/viewer/2022032801/56649d545503460f94a31112/html5/thumbnails/30.jpg)
For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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For slideshow: click “Research and Talks” from www.calstatela.edu/faculty/mkrebs
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Therefore theGolden Ratiois irrational.