Why is the Euclidean metric called the prime at infinity?

Question

I've been studying p-adic analysis recently and after a bit of searching on the web, I haven't found an answer as to why the Euclidean metric is referred to as the 'prime at infinity', and given the suggestive notation of $|\cdot |_{\infty}$. Does the p-adic metric for larger and larger primes serve as a better and better approximation of the Euclidean metric, or is it something else?