There's a formula: another = an + other. Think of it as of an article plus the word "other" that have historically merged into one word. Grammar requires some article before "other book"; either "the" or "a." Depending on the context, you get either "You need to buy the other book" (if, for instance, the guy bought only the first book out of the set of two) or "You need to buy an_other book ...
I thought this might have already been asked, but apparently not. Is using the phrase "one another" considered equivalent to the phrase "one and other"? Is one of the two considered right and the...
conjunctions - "One another" or "one and other" - English Language ...
The formal discourse marker used by the OP; "on the one hand ... on the other hand" expresses two contrasting ideas, opinions or facts. In view of this fact, I suggest the following alternatives:
Alternatives to the "on the one hand... on the other hand" construct
According to this, as "other" is an adjective you must write "two other places", "the two other places". In this ngram you can see that this order is prevalent. There is a very small minority (the other two sides, the other two groups, the other two men) but for these three words this is nonetheless by far the preferred order.
I have seen a statement: We have a Christian duty to serve each other. Is this statement correct? Because 'each other' is used for two persons and 'one another' for more than two persons.
Both these expressions idiomatically mean exactly the same thing, that any number of people or things went in a series, one at a time, each following the previous. Cambridge dictionary states this: one after another (also one after the other) many, in a series Neither variation suggests how many are in the sequence, or limit it to a number.