Properties of Natural Numbers

1. Write down the largest natural number you can using only 5 standard symbols (such as numerals and operation symbols.
2. The famous "Four Fours" problem: Express each of the natural numbers from 1 to 100, using exactly four 4's and any number of standard mathematical symbols. For example, ; .
3. One person names three properties of natural numbers. Another tries to name another mathematical structure that also satisfies these properties. Repeat. How many properties are needed to pin down the natural numbers?