Cardinal number of the Banach space $c_0(A)$

Question

For infinite dimensional Banach space $X$, the cardinality of $X$ is equal to its algebraic dimension. Now let $A$ be an infinite set and define $c_0(A)=\{f:A\rightarrow\Bbb R, f$ is bounded and $ \lim_{x\in A}f(x)=0\}.$ We know that $c_0(A)$ is a Banach space with $\|.\|_{\infty}$. Now, what is the algebraic dimension of $c_0(A)?$ (or equivalently, what is the cardinality of $c_0(A)$)