Theories of Arithmetic

Theories of Arithmetic are logical frameworks that explain how basic numbers and operations, like addition and multiplication, work consistently. They aim to define the properties of numbers so mathematicians can agree on what is true about them. For example, they rigorously prove that adding 2 and 3 always equals 5, based on set rules. Different theories vary in their complexity and assumptions, balancing simplicity and completeness. These logical systems help ensure that mathematical statements are valid and unambiguous, providing a solid foundation for all of mathematics.