One is... and the other...

The other is used to refer to the second of two things/people:
- I have two customers: one is Italian, the other is German.

Another is used to refer to a person/thing when there are more than two choices:
- I didn't like the handbag and I asked the shop assistant to show me another one (there are more than two bags in a shop).
- I still don't understand the rule. Could you give me another example?

So, the first sentence is correct.

I'd disagree slightly with Tania's examples. "The other" isn't necessarily only used with two things/people. There can be any number of them but "the other" specifies the last remaining one to be discussed :

I have three brothers : One lives in Italy, one in Germany and the other in the States.
With this example I could also say ... another in Germany and another in the States. With more than two I have the choice of whether to present them all as indefinite or the last as definite.

In Tania's examples of the handbag and example , the indefinite form is used because I am not asking for a specific handbag/example but any handbag/example the person wants to give me.

So basically, the choice between another /the other is exactly the same as the choice between the indefinite and definite articles with any other noun phrase. If I'm talking about something specific, then "the" :
I don't like these pens. Give me the red pen / the other pen.
I don't understand this rule. Give me a clearer example /an easier example / another example.

The fact that the indefinite article "an" is written together with "other" to form one word, doesn't change the fact that really it's just an "ordinary" indefinite article + noun phrase construction - though the noun is often elided (omitted) because it's understood in the context, as in :

I have three brothers : one lives in Italy, another (brother) lives in Germany, and the other (brother) lives in the States.

Sue, thanks for corrections and clarifications :-)

Thank you, Sue.

[IMG]http://www.aaapostcards.com/cards/fullsize/298.gif[/IMG]

Hi Sue,

Student Fees Protests In London, Birmingham, Glasgow, Manchester And Cambridge: Disorder Breaks Out | Politics | Sky News

Two men were arrested on Tuesday on suspicion of violent disorder, one in Leicester and another in London.

Is another correct? Isn't "the other" correct?

No, it's fine. As I've said before - grammar gives us ways to express meaning, and it's up to the speaker/writer to decide which meaning s/he wants to express. Here the writer has chosen to express both as "indefinite" - they've not yet been named, so s/he's not yet seeing them as "specific". Of course, as s/he has specified "two men", s/he could see the other as having been specified and choose to say "the other". In fact, if you read what i wrote above, that's what I was assuming would happen. But in fact, it's always a choice, and this writer chooses to see them as still indefinite.

No, it's fine. As I've said before - grammar gives us ways to express meaning, and it's up to the speaker/writer to decide which meaning s/he wants to express. Here the writer has chosen to express both as "indefinite" - they've not yet been named, so s/he's not yet seeing them as "specific". Of course, as s/he has specified "two men", s/he could see the second as having been specified and choose to say "the other". In fact, if you read what I wrote above, that's what I was assuming would happen. But in fact, it's always a choice, and this writer chooses to see them as still indefinite.