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After explaining something you wish to give an example. You write "Here is an example."

Is "Here is an example." the last line of the paragraph explaining the idea or is it the first line in the next paragraph?

I can't imagine that the example would itself be included with the explanation. It would be too long and is seems like such a natural place to break.

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It's neither, it's a floating sentence. Where you place it is up to you. I always place it after the previous paragraph for clarity, and to treat the example as its own entity.

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It is usually more effective to place the example as a separate sentence, and indent it farther to set it off.

However, regardless whether you separate the example, the introducing sentence would end with a colon:

  • Here is an example:

Note that you do not use a colon if you refer to the example less directly; e.g.,

  • An example is shown below.
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