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I have re-posted this to test my changes to the latex2wp.py and terrystyle.py programs, compiled with Python Software Foundation’s Python 2.7.2 64 bit version, to add support for LyX 1.6.9. The code change incorporates some additional theorem-like environments, macros, font styles, and the numbering has been change so that the different theorem-like types each have a separate counter (e.g., theorem 1, theorem 2, lemma 1, proposition 1, theorem 3, lemma 2, …, as opposed to theorem 1, theorem 2, lemma 3, proposition 4, …). Furthermore, I have provided more background information which will benefit those without a background in abstract algebra.

Proofs from THE BOOK by Martin Aigner and Günter Ziegler begins by giving six proofs of the infinity of primes. The first proof is what they call "the oldest Book Proof" attributed to Euclid. Before we go over this proof, lets cover some background. Read the rest of this entry »

Proofs from THE BOOK by Martin Aigner and Günter Ziegler begins by giving six proofs of the infinity of primes. The first proof is what they call “the oldest Book Proof” attributed to Euclid. Before we go over this proof, lets cover some background. Read the rest of this entry »

Proposition 1 Prove ${\sqrt{2}}$ is irrational.

Here is a proof using a traditional method (See Euclid’s Elements Book X which incorporates Theatetus work on incommensurable numbers. It includes a proof that ${\sqrt{2}}$ is irrational (Proposition 22), and ends with a proof that there are infinitely many distinct irrational numbers (Proposition 115): Read the rest of this entry »