And on today’s “Fun with functions” … I’ll explain how to ruin a dinner party with a maths joke:

“There are two types of people the world: those who don’t understand my humour”.
— Mike Haseler (@scotpolitik) February 14, 2018

It is often said that any joke that has to be explained is ruined. However in this case, that might be the joke. So, to add to the excruciating nature of the joke here is my explanation.
There is another joke that goes:

“There are 10 types of people in the world, those that understand binary and those who don’t”.

That of course is what is being referred to by the “two types of people”. However, note that to accurately reflect the original joke it would need to be 10 types of people. That is why this is such a classic. Because you could use the “10” types of people for any base and have three groups:

“there are those who understand binary, those who don’t, and those who know there are more bases than binary and decimal”.

And of course, the number of possible groups can be extended even further … indeed up to an infinite base.
However a base 1 joke  is unique. Because there is only one number in a base one number system and that number is obviously zero.
So, clearly, we could have the joke of the form:

“There are 10 groups of people in the world: those who don’t understand base 1”.

That then fits the general patten of 10 jokes. Thus the humour in this joke is that “two” spelt out as a word does not work. It is clearly wrong – the teller was so bad at jokes they couldn’t even tell it properly. But then again, the pun on “10” only works when written not when spoken. And “those that don’t understand my humour” is only one group. So, the statement is clearly right, because how can anyone understand a joke that is palpably based on false logic and utterly wrong.
And that is the joke …
Which then, when you get it, makes the statement that there is only one group of people false … and it stops being funny.

No, No, No!
Sorry … just kidding!

The real joke is that’s its a a pun on function and dinner part and that the idea that anyone who thought the joke was funny would be invited to a dinner party in the first place.