How to list some examples? "such as", "i.e.", "etc.", I'm always confused with these words. also, what's the difference between "example" and "sample", give me some examples, thanks!
Isn't the abbrevation for "for example" -> e.g. (exempli gratia)?!

"i.e." stands for "that is to say" ("id est") - and is therefore used when explaining something you've just said a bit more detailedly.
Such as and i.e. are good ways to begin a list of examples. Etc. should come at the end of the list. It indicates that the list continues in a similar way. Here's an example:
"You should use only positive, odd-numbered integers, such as 1, 3, 5, etc." You probably shouldn't use 'etc.' unless you're referring to a list of things that most people are familiar with.

'Sample' and 'example' come from the same root word. I believe that a sample is a selection of things from a larger set, whereas an 'example' is one element of the sample. So, if I'm writing about all odd-numbered integers, my sample could be all positive odd-numbered integers with a value less than 11, and my example could be 5.
SET-->Sample-->example. General-->specific.

Sorry about all the mathematics language.
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 Pemmican's reply was promoted to an answer.
You're right, Pemmican. I am a fraud!