Numbers are a journey from "Zero" to "Infinity"

INFINITY:

Infinity is an abstract concept that describes anything without limit. One only has to imagine the sky to imagine that space may go on forever.

Philosophically there are three different types of infinity

• Potential or mathematical infinity: a process which has the potential of being infinite. For example, counting the natural numbers 1, 2, 3, 4, 5, ... is a potentially infinite task.
• Actual or physical infinity: an infinity which exists in nature. This category includes the infinitely large and the infinitely small. Examples of physical infinities would include the Universe (if it is infinite in space) or Time (if it is infinite).
• "Absolute" infinity: God.

We are going to talk about the mathematical infinjity.

The word “infinity” derived from the latin word “infinitas” that means unboundedness and Greek word “ apeiros” meaning endless.

INFINITY is treated as a number as it counts or measures things but it is not a number like all other real numbers.

HISTORY

The ancient Indians and Greeks, unable to codify infinity in terms of a formalized mathematical system, approached infinity as a philosophical concept.

The symbol of infinity was used by the Romans to express large quantities. It was “John Wallis” who was the first mathematician to use the symbol to denote an infinite quantity.

In mathematics, the infinity symbol is used more often to represent a potential infinity rather than to represent an actually infinite quantity such as the ordinal numbers and cardinal numbers (which use other notations). For instance, in the mathematical notation for summations and limits such as 

The infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large (towards infinity) rather than actually taking an infinite value.

In other areas than mathematics, the infinity symbol may take on other related meanings; for instance, it has been used in book binding to indicate that a book is printed on acid free paper and will therefore be long-lasting.

In mathematics it is used in:

Calculus

 Lebinitz one of the co-inventors of infinitesimal calculus speculated widely about infinite numbers and their use in mathematics. To Leibniz, both infinitesimals and infinite quantities were ideal entities, not of the same nature as appreciable quantities, but enjoying the same properties.

Real Analysis

In real analysis, the symbol  , called "infinity", denotes an unbounded limit.

Complex Analysis

As in real analysis, in Complex anaysis the symbol

 , called "infinity", denotes an unsigned infinite limit  

means that the magnitude

 of x grows beyond any assigned value.

Set theory

A different form of “infinity” is the ordinal and cardinal  infinities of set theory. Georg Cantor developed a system of transfinite numbers in which the first transfinite cardinal is aleph null, the cardinality of the set of natural numbers.

Exploring the infinite is a journey into paradox.