Different leave campaigners seem to give different numbers for how many presidents the EU has. That gives a good idea as to how much they value truth and accuracy.

I've never been able to work out why the number of "presidents" is a reason to leave (or not). It seems to be something to use to mock the EU. But all it really does is demonstrate how badly they understand the EU and how it works.

Let's make this clear. There is no "President of the EU".

There are 4 key political institutions in the EU; the European Parliament, the European Commission, the European Council, and the Council of the European Union (or Council of Ministers). Each of these needs a chairman to coordinate discussions and debates, just like the Speaker of the House of Commons or the House of Lords. These chairmen are called "Presidents" of their respective institutions in English. "Chair" would have been a better name in English, or "Speaker" for consistency with the UK parliament, but now we're stuck with "President".

A slightly imperfect translation isn't a reason to leave the EU.

None of these "presidents" are presidents of the EU any more than the speakers of the Houses of Parliament are the presidents of the UK.