As we are approaching the end of our Math Symbols and Their Meanings series, we are also wrapping up the difficult side of mathematical language. Last time we dealt with Linear and Multilinear Algebra which mostly applies to high-dimensional geometry. In this article, we return to numbers, more specifically to infinite numbers and their operations, part of set theory and calculus.

**Infinity Concept In Mathematics**

The concept of infinity “∞” in mathematics holds various meanings:

- Endless sets of numbers;
- An indefinitely great number or amount;
- A value greater than any finite numerical value;
- A distant ideal point at which two parallel lines are assumed to meet;

The history of this endless concept can be traced back to Pythagoras in geometry, however, it was approached as a more definite theory by Georg Cantor. He came up with the idea that infinity is much more complex than a neverending story: there are different sizes of infinity when it comes to the set theory of natural numbers. Before getting into this, let’s look at the fundamentals of infinite numbers.

**Basic Symbols For Infinite Number Sets**

#### Convergent Series

#### Divergent Series

#### Transfinite Numbers

*n*< ℵ0 for each

*n*∊ ℕ and ℵ0 < ℵ.

There are also “surreal” numbers that indicate an ordered, proper class with real numbers including infinite and infinitesimal numbers, larger or smaller than any positive real number. But enough of confusing infinite numbers that grow and continue forever.

#### Aristotle’s Infinite Series

*A*, A0,… , An, … ,

### Georg Cantor’s Infinite Series

- Enumerable infinite series – defines a set of elements that can be paired with a natural number and form a countable set.
- Non-enumerable infinite series – defines the sets of rational and real numbers, because the sets of rational and real numbers will always be incomplete according to Georg Cantor’s findings.

If you want to dive deeper into Cantor’s interpretation of infinite series, check this out.

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