-
The Peano axioms are a set of rules that define the natural numbers (like 0, 1, 2, 3, and so on) in a logical way. Here’s a simplified explanation: 1. There is a first number: There is a number called zero, and it is the starting point for all natural numbers. 2. Each number has a next number: Every number has a unique “successor,” or the number that comes after it (like 1 comes after 0, 2 comes after 1, etc.). 3. Zero is special: Zero is not the “next” number of any other number. This means the sequence of natural numbers doesn’t loop back to zero. 4. No two numbers are the same if they have different successors: If two numbers have the same “next” number, then they must actually be the same number. 5. Patterns hold for all numbers: If something is true for zero, and it stays true when moving from one number to the next, then it must be true for all numbers. These principles lay the groundwork for understanding and working with the natural numbers systematically.