#cantor set

Alexander Horned Sphere | James W. Alexander (1924)

(It’s Always) Sunny set up. 

My mind when i try to solve 1+1

CANTOR SETS - BASIC SELF-SIMILARITY  The work of Georg Ferdinand Ludwig Philipp Cantor [1845 – 1918] – German mathematician and, in the latter third of the 19th century, the inventor of set theory, now a fundamental theory in mathematics.

IMAGES Simple Cantor Set  [explained below] 3D Cantor Set (by Oppenheimer on deviantArt)  [Cantor dust] Cantor Set, 2004, digital c-print (by Kevin Van Aelst)

Constructing the Cantor Ternary Set The Cantor ternary set is created by repeatedly deleting the open middle thirds of a set of line segments, as follows.

Start with a line segment – for example, the line [0,1] in the top row of the first image.

Cut this unbroken line into three identical parts.

Delete the middle of the three parts.   This leaves what you see in the second row. 

Repeat:   Cut each of the two lines in the second row into thirds and then delete the middle third of each of the two lines. This creates the third row.

Repeat ...  [X]

The Cantor set is the prototype of a fractal. It is self-similar, because it is equal to two copies of itself, if each copy is shrunk by a factor of 3 and translated.

Anytime I think about the Cantor set...I have overwhelming to start chanting in Latin.

Beyond that, meh? I MEAN IT'S A USEFUL EXAMPLE OF A NOWHERE DENSE SET? But like beyond that...*yawns*.