organic chemistry - What criteria have to be met to term a carboxylic acid a 'fatty acid'?

So we were doing the chapter Biomolecules in class the other day, and my teacher told us that every carboxylic acid that consists of an aliphatic chain and a total carbon atom count that's four or more, is a fatty acid.

Now owing to my teacher's (rather annoying) habit of grossly over-simplifying things, I decided to look up 'fatty acids' in my trusty Oxford Science Dictionary (printed in 2003). According to it,

Chain length ranges from one hydrogen atom (in methanoic acid) to nearly 30 carbon atoms.

But a quick Wikipedia search, gives me this:

Most naturally occurring fatty acids have an unbranched chain of an even number of carbon atoms, from 4 to 28.

So now I'm completely lost. Fine, chuck what my teacher said, but the other two sources seem to contradict each other. So I'd really appreciate it, if someone can help me get the following straight (I'd prefer a reliable source, if you're citing anything):

Q1: What is the minimum number of carbons in a carboxylic acid as a whole (includes the carboxyl group)? So is methanoic acid or butanoic acid that's the smallest fatty acid?

Q2: Is there an 'upper limit' on the total carbon atom count for fatty acids? As in; can I synthesize, say, an 80 carbon aliphatic carboxylic acid and still correctly call it a fatty acid?

Q3: Is there any other criterion that's necessary to classify something as a fatty acid that hasn't been mentioned by my teacher or the other sources? If so, what is it?

Answer

I suggest to consult the IUPAC Compendium of Chemical Terminology, aka the Gold Book for a definition of fatty acids!

In a narrow sense, fatty acids are defined as

aliphatic monocarboxylic acids derived from or contained in esterified form in an animal or vegetable fat, oil or wax.

The definition continues to mention that

natural fatty acids commonly have a chain of 4 to 28 carbons […]

The paragraph closes with a wider definition, namely:

By extension, the term is sometimes used to embrace all acyclic aliphatic carboxylic acids.

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Personally, I have used the term fatty acids only for natural fatty acids.