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Why 1+1=2: A proof with axioms of first-order mathematical logic

Everyone knows that 1 + 1 =  2.  But why?  Is there some sort of universal law that makes this always true?  It was only in relatively recent history that the fundamentals of mathematical logic began to be outlined explicitely.  Some of the most important work here was done in the 19th century, when Guiseppe Peano discovered a set of axioms that explain the very logic behind number theory (arithematic) itself.  Referred to as "Peano's Arithematic" or first-order mathematical logic, the principles can be summarized into a few simple axioms, plus one more axiom that is a little more complex, known as the "rule of mathematical induction", which I will not get into here.

"Cur nunc Latinam studeo": but why now?

So, my new spontaneous interest is to learn Latin.  But why?  What could I possibly gain from that?  Not much, I guess, but then again, what do I really gain from creating algorithms for generating mazes on n-sided polygon tessellations?  The answer is simple.  I have long enjoyed, and have been very good at, studying and learning languages, but... I don't enjoy talking to people.  Latin is a dead language.  Thus it is the obvious choice.

An overview of Russell's paradox

This will be the first in a set of two articles about Russell's paradox.  Russell's paradox, discovered in 1901 by mathematitian Bertrand Russell,  is an antinomy that illustrates that certain attempted formalizations of naive set theory lead to contradiction.  Most simply, it is defined as:

Soaring pantless through the forest: an experience in social nudism

The mission was simple.  There were 4 bananas in the kitchen across the park that required retrieval.  Two minutes later, I found myself completely naked, dashing through cold rain in the dark, carrying a floral-print umbrella, transporting four bananas on whose skins someone had written their name in red marker.  In the distance another gentleman stood under his umbrella, pantless. An overwhelming thought came into my head... "My god, if I were to describe this event to someone, some context would certainly be necessary lest I be perceived as completely, totally, insane."

Maze generation on n-sided polygon grids

I wanted to see if a maze could be generated on a grid that is not made of rectangles, but instead of various interlaced polygons.  In two dimensions, of course, triangles and hexagons are the only geometries that make sense.