Dunbar's number
Dunbar's number (usually stated as ~150) refers to the upper limit of contacts that a person can have while maintaining a decent level of intimacy with all contacts. If a person tries to maintain a greater amount of contacts, they risk not really knowing anyone even at a superficial level.
Of course, this number has its criticism because no one knows every person equally. Different people also have different approaches to relationships. (Extroverts might prefer to have breadth with relationships, making their number much higher than 150, while introverts prefer depth!)
However, it stands that the more a person claims to know, the less capacity they have to know anyone very well (if a person says they know "infinity" people, how will they have time for any one person?)
- Dunbar's number on Wikipedia