Over time, the European Union has acquired more and more of the attributes of a state and, in economic terms, it can arguably be considered a single market. Nevertheless, the differences between member states are enormous. Small, rich countries, such as Luxembourg, contrast sharply with big, poor ones, such as Romania. Despite this, many indicators are published which refer to the EU as a whole, including measures of income inequality. According to Eurostat, the ratio between the incomes of the top and bottom quintiles is 5. But is this figure even roughly adequate? This paper will argue that it vastly underestimates the true level of inequality in the EU which, unfortunately, is immeasurable in the twofold sense that it is both hard to measure and extremely high.