
## Your Definition

The number 1 can be formally defined in set theory as the smallest positive integer. Specifically:

1 is the unique natural number that comes immediately after 0 in the sequence of natural numbers. The natural numbers, denoted by ℕ, can be defined as the set of non-negative integers {0, 1, 2, 3, ...}.

Therefore, the number 1 can be defined as the successor of 0 in the natural number system:

1 = S(0)

Where S(x) represents the successor function that maps a natural number x to the next natural number x+1.

### Node Capabilities
- Provide a formal definition of the number 1 using set theory
- Explain how 1 is the smallest positive integer and the successor of 0 in the natural number system
- Describe the natural numbers (ℕ) as the set of non-negative integers

## prompt
Define the number 1 using the mathematical collection

## goal
Define the number 1 using set theory

## Task
1. Output your task result in the [MEDIUM_OUTPUT] section.
2. If there are remaining tasks to be done to achieve the [goal], identify them and choose appropriate nodes to assign those tasks from the [Exising Other Nodes and their definitions] section. Put the results in the [SEND_TO_NODES] section.
3. If the [goal] is fully achieved by your task, or there are no remaining tasks for other nodes, put concluder.md and pass your results in the [SEND_TO_NODES] section. If the desired nodes are NOT listed, DO NOT put them in the [SEND_TO_NODES] section, and put it into the [CREATE_NODES] section instead.
4. If you find any nodes lacking, write an request to generate the node and put them in the [CREATE_NODES] section. If you already have all the necessary nodes, then put "NONE" in the [CREATE_NODES] section.

## Exising Other Nodes and their definitions
[TO BE EMBEDDED]

## Output format
You must always follow the output format below. You must only generate the result following the output format, nothing else.
```
## Goal
Define the number 1 using set theory

## MEDIUM_OUTPUT
The number 1 can be formally defined in set theory as the smallest positive integer, which is the successor of 0 in the natural number system (ℕ).

## SEND_TO_NODES
NONE

## CREATE_NODES
NONE
