Can a "claim" have the same meaning as the word "sentence"?

Question

Yes, in this context: A claim is a sentence that assets something to be true.

2) I am innocent of the crime
3) The moon is made of green cheese
4) A sentence can be a claim.
5) Saddam Hussein is developing nuclear weapons.

More information on claims:

http://www.uncp.edu/home/canada/work/markport/best/writing/argument.htm
Scroll down for the section on claims.

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Read the first three paragraphs.

http://pubpages.unh.edu/~dml3/guidefor.htm
Scroll down and read about the thesis.

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