1

1 (one) is a positive integer following 0 and preceding 2. Its ordinal form is written "1st" or "first."

Properties
1 is the multiplicative identity, meaning that \(a = a \times 1\) for all \(a\). In fact, \(a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_n 1 = a\) (arrow notation) for all \(n \geq 1\) and \(a\), so 1 is a sort of identity for all the hyper operators beyond addition. 1 appears frequently as a "default" argument in googological notations, such as BEAF, chained arrow notation, and hyper-E notation.

1 is. It is the only positive integer which is neither prime nor composite.

1 is a, , , etc.

1 is the 1st Busy Beaver number.

In googology
Sbiis Saibian argued that all numbers larger than 1 should be called "large numbers," because the reciprocals of large numbers are small. The large numbers and small numbers are "mirrored" about 1, so it makes sense to say that 1 is the threshold of largeness. A number like 1 + 1/googol could be called a "very small large number." The smallest large number, obviously, also can't exist.