I have a card called Solidarity, reading:
If you have only 1 original Type of monster in your Graveyard, face-up monsters you control with the same Type gain 800 ATK.
In the case where the graveyard has two or more creatures of the same type then it's obvious we can use the effect; similarly, if the graveyard has precisely one creature in it, then it has exactly one type of creature in it (and so the effect may be applied).
But if the graveyard has no creatures in it, I would argue that there is exactly one type of creature in it (this is a vacuous truth). I wanted to use the card in this situation but my opponent absolutely refused it.
To me this truth is as valid as saying the Empty Set is Hausdorff. I'm hoping there are mathematicians out there that also play Yugioh and are qualified to answer this; alternatively, I am hoping there is an official answer to this, not just some opinions.