Section 11 due 28 September

"Proposition 11.6. One of the digits of 2 = 1.414213562 . . . occurs infinitely many times.

Proof. There are only finitely many possible digits {0,1,2,3,4,5,6,7,8,9}
but there are infinitely many decimal places. QED"

It seems to me that this proof isn't complete without at least mentioning the pigeonhole principle. They do address it in the explanation after the proof, but since it isn't included in the proof itself, I am not in convinced that this proof is complete. Is it? If so, why? Would this get full credit on the homework/test?

I don't understand the proof of proposition 11.7.


The formatting is so weird. Sorry if the font randomly changes sizes.

-Batman