What is the relationship between fame and infamy?

In layman's terms, what is the relationship between fame and infamy? Is fame required to be infamous? Are they (definitively) mutual exclusive?


Solution 1:

Fame is any kind of fame. Osama bin Laden and Steve Carell are both famous. Only bin Laden is infamous.

Solution 2:

Infamous:

Well known for some bad quality or deed.

Whereas famous is just "well known". So everyone who has infamy has fame, but not everyone who has fame has infamy.