Currencies in Pairs?

Often new traders struggle to grasp the concept of trading currencies in pairs, why not just buy the Euro they might ask? Why does it have to be paired with the US Dollar? Simple, the currency on the right side of the pair is there to establish a comparative value, without it how could the base currency (currency on the left side of the pair) have any certain value? In other words, if currencies were not paired what would a single currency gain or lose value against? By pairing two currencies against each other a fluctuating value can be established for the one versus the other. So, how is the Euro doing against the Dollar, or how many Dollars does it take to buy one Euro? Thus the need for currencies in pairs.