Existentialism Mathematics #05

March 17, 2010

Notes on Existentialism Mathematics by dr. Algirdas Javtokas (New Frontiers in Mathematics Series).

.

Lemma 1. 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 01 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 01 0 0 0 0 1 11 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.

0 1 1 0 1 010 1 1 0 1 0 1 0 1 0 1 0 1 0 1 010 1 1 1 1 1 1 0 0 0 0 0 01 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 011 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 0

.

Proof  1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 11 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0

0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0

00 \subset 00100 \subset 000

.

Lemma 2. 0 1 1 0 1 01 0 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 00 1 0 1 0 1 0.

0010100 + 00 + 00 + 00 = 000

.

Proof  1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 11 0 1 0 1 0 0 1 1 0 1 01 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1

0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1

000 \Rightarrow 000

0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 11 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 01 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1

.

Theorem. 0 1 01 0 1 0 1 0 0 0 0 1 11 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1

000 + 000 + 000 + 000

1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1

.

Proof  0 1 01 0 1 0 1 0 0 0 0 1 11 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 00 1 0 1

00000010101011000 + 000 \le 000 \le 000

0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0

0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 01 0 1 0 1 01 0 10 1 0 10 1 0 10 1 0 1 00 1 1 1 1 1 0 0 0 0 0 0 0

0 1 01 0 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 0 0 1 1 0 1 01 0 1 0 1 0 0 0 0 1 1 1 1 0 00 1 0 1 0 1 01 1 0 1 01 0 1 0 1 1 1 1 1 1 1 1 1 1 101

.

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One Response to “Existentialism Mathematics #05”


  1. your communication and soft skills are very good.are you actually in customer relations field in your real life?maybe not, but you exactly know how to connect with your readers.


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