There is also a problem: The term "even" meaning "integer multiple of two" is a convention; people agreed on it. It is not a formal definition. Another case where people used a convention they agreed on was that of prime number: Before the 20th century, there were many inconsistent definitions of prime: Mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime. The modern definition of "prime number" is "positive integer with exactly 2 factors", so 1 is not prime. This definition is rational: it naturally suits mathematical theorems that concern the primes. For example, the fundamental theorem of arithmetic is easier to state when 1 is not considered prime