I'm wondering whether to use a colon, semicolon or comma in the following sentence.
I've come to a tough conclusion: The second book is better than the first.
Is that correct? Or would a semicolon or comma work better?
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The colon is correctly used (it is placed where the word 'namely' could be used instead), and positioned (it follows words that could stand alone as a complete sentence, and precedes something directly related). The first word after a colon is never capitalised if it does not start what would be a complete sentence, and many style guides advise against capitalising it even if it does, unless the first word is a proper noun or something else that is always capitalised. If you are writing for publication or as an academic submission, it is best to conform to whatever style guide is applicable. Otherwise, feel free to choose, remembering to be consistent.
Two sentences can be placed one after another using a semi-colon. That is one of the main reasons to use one. The semi-colon is used in place of a conjunction.
1) I've come to a tough conclusion and the second book is better than the first.
That would be a compound sentence. It's fine. It is one option if you want both sentences to have equal weight.
2) I've come to a tough conclusion; the second book is better than the first.
That's fine. Both have equal weight and is another way to express it.
3) A colon shows that what comes after it is the conclusion that can be derived from the first statement.
I've come to a tough conclusion: the second book is better than the first.
What comes after the colon expresses the conclusion you've come to, and is your main point.
I would not use a comma as there are two complete sentences to deal with and a comma is not usually used for dealing with that given the ideas in them.