> If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are fr

> If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends. In pragmatics (a subfield of linguistics) this is called "conversational implicature" - in particular it's an example of the "maxim of quantity". Which is to say, you are correct about how the language works and mathematicians are a little weird.