Let $\kappa, \lambda$ be cardinals such that $\lambda > \kappa \geq \omega$. I'm trying to show that the set of finite partial functions from $\kappa$ to $\lambda$ has cardinality $\lambda$.
It is remarked here that this is the case, but I can't seem to see why.
Clearly there are at least $\lambda$ many such finite partial functions. This gives a bound from below.
But a finite partial function from $\kappa$ to $\lambda$ is also just a finite subset of $\kappa\times\lambda$. Elementary cardinal arithmetic yields $(\kappa\cdot\lambda)^{<\omega} = \lambda^{<\omega} = \lambda$ which gives a bound from above.