Can someone simplify the differences between intensional and extensional definitions for me?

Question

I'm having a really hard time grasping the concepts.

Wow just when I thought the differences I already have from my professor couldn't get anymore obscure....

(Again, can someone who actually understands this concept, not one who regurgitates wikipedia, explain it to me in simplifed terms?)

Answer 1

I use the mnemonic "ICED" to remember that 'I'ntention 'C'onnotes attributes, and 'E'xtension 'D'enotes class members.

For example, the intention connoted by the term 'dog', would be the attributes that the term connotes, such as 'having four legs', and so on.

The extension denoted by the term 'dog' would be all of the class members of the term; such as Lassie, Fido and all the dogs in the universe.

Answer 2

A = {2, 3, 5, 7} defines set A by extension, simply by listing its members.
A = {primes less than 10} defines set A by intension, by describing the properties necessary to be members of the set. see link.