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In formal writing, if I have 2 examples to depict what I said earlier, can I start writing a sentence using 'for another example' form after explaining my first example using 'for example'? More clearly:
for example, bla bla bla.... .
for another example, bla bla bla ... .
is this construction suitable in formal writing?
You should not say for another example.
The phrase for example does not tell the reader what you are about to say, it tells the reader why you are saying it. This is why we use the preposition for, just as we might say for better understanding or for comic relief, and it is why we do not say for an example. Example is not used as the 'countable' noun but as a generic quality attributed to what follows: it exemplifies what has gone before.
In formal writing or speaking, there's no need to put for for the second time when it's quite obvious that you are mentioning one more example.
For example: blah...blah...blah...
(And...) Another example (is): blah...blah...blah...
"For example" is used before mentioning an example:
Many countries, for example Japan and Mexico, has a lot of earthquakes
To mention other examples you may say "As another example, balah blah.."
For example, blah blah blah... As another example, blah blah...
I would go with something like this:
For instance... Another example would be...
This will help avoid repetition.
