For some authors and thinkers, the infinite is an impossible dream, a chimera, a chaos, and even a vertigo. Aristotle split the concept of the infinite in two arguments: the actual infinite, and the potential infinite. For the actual infinite he argued that there cannot exist an infinite body, but for he accepted the idea of a "potential infinite".

The idea of the infinite remained for a long time in the realm of the speculative, and the mystical.

But about a century ago, Georg Cantor took the the concept of the infinite to a different twist: Can there be more than one type of infinite?

For some authors and thinkers, the infinite is an impossible dream, a chimera, a chaos, and even a vertigo. Aristotle split the concept of the infinite in two arguments: the actual infinite, and the potential infinite. For the actual infinite he argued that there cannot exist an infinite body, but for he accepted the idea of a "potential infinite".

The idea of the infinite remained for a long time in the realm of the speculative, and the mystical.

But about a century ago, Georg Cantor took the the concept of the infinite to a different twist: Can there be more than one type of infinite?

Why are spirals so appealing? Why are they are used so frequently in poster designs, in architecture, in photo compositions, in religious symbols?

Not all spirals extend inwards and outwards in the same way. The Archimedean spiral is probably the most common, ancient and easiest to construct. This type of spiral is also the most commonly found in nature.

But there is also another type of spiral –the spiral called the logarithmic spiral– that has a lot of interesting mathematical properties.

Mathematics is a symbolic language. To understand mathematics, we must get acquainted with its symbolism.

Mathematical symbols are shortcuts to language expressions like: "is a subset of", denoted by the symbol "⊂", or "is greater than", denoted by the symbol ">".

There are hundreds of mathematical symbols, but the good news is that all of them keep their meaning no matter the field of math you are working with.

Georg Cantor laid the foundations of a beautiful mathematical theory called the Theory of Sets. Some sets are finite while other sets are infinite. Cardinality is the measure that separates one type of set from the other.

Finite sets are intuitively easy to understand: finite sets must be those sets with a "countable" amount of elements. So far, ok. The problem arises when we try to apply a simple definition like the above to infinite sets.

For the layman with basic mathematical tools, an infinite is an infinite and there's nothing else beyond that; but there are some mathematical constructs that go beyond this: there are an infinite amount of infinites, each one "greater" than the other.

Tetration is a mind-boggling mathematical operation. The grains of sand needed to cover our entire Milky Way is easily expressed using tetration.

In school and college we learn and refine the usual math operations of addition, subtraction, division, and exponentiation. We learn that subtraction is a form of addition, multiplication is repeated addition, and exponentiation is a repeated multiplication. Is then tetration a repeated exponentiation?

What is tetration, why is it so mysterious, and why it is seldom mentioned?