Give an example of an integral domain which has an infinite number of element yet its finite characteristics Give  an example  of an integral domain   which has an infinite  number  of element yet its  finite characteristics?

I thinks $\mathbb{Q}$

Is  it correct ??
Take $F := \mathbb{F}_p(x)$, the field of rational functions in one variable over the prime field $\mathbb{F}_p$.
X is a set of infinity elements . Then P(x) is also infinity . And P(x) with respect to symmetric difference &amp; intersection forms a infinite integral domain with Cher 2