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===Proof that π does not contain π:===
 
===Proof that π does not contain π:===
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1) Let &pi; be represented by the sequence of digits x<sub>0</sub>.x<sub>1</sub>=1, x<sub>2</sub>x<sub>3</sub>x<sub>4</sub>x<sub>5</sub>......
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1) Let &pi; be represented by the sequence of digits x<sub>0</sub>.x<sub>1</sub>x<sub>2</sub>x<sub>3</sub>x<sub>4</sub>x<sub>5</sub>......
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Therefore x<sub>0</sub> = 3, x<sub>1</sub>, x<sub>2</sub>=4, x<sub>1000</sub>=9, and so on.
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Therefore x<sub>0</sub> = 3, x<sub>1</sub>=1, x<sub>2</sub>=4, x<sub>1000</sub>=9, and so on.
    
2) Assume that &pi; contains &pi;: Then there is an index <i>n</i> such that x<sub>0</sub> = x<sub>n</sub> = 3,
 
2) Assume that &pi; contains &pi;: Then there is an index <i>n</i> such that x<sub>0</sub> = x<sub>n</sub> = 3,
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