# Conclusion

Pronunciation: /kənˈklu.ʒən/ Explain

The end product of a set of mathematical arguments is usually a conclusion.[2] The conclusion states what the writer claims is a reasonable inference given the arguments. The basic outline for a direct proof is:

1. Claim: What the writer says will be proved by the arguments.
2. Arguments: A set of arguments based on previously proved theorems, axioms, and definitions.
3. Conclusion: Statement that the claim has been proved.

A conclusion is also part of a logical if-then statement. The format of a if-then statement is: "if condition then conclusion". The conclusion is a reasonable inference given the condition. An example of a logical if-then statement is: if a > 5 then a > 4.

### References

1. McAdams, David E.. All Math Words Dictionary, conclusion. 2nd Classroom edition 20150108-4799968. pg 41. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Atwater, Lymon H. Manual of Elementary Logic. revised edition. pp 24-25. www.archive.org. J. B. Lippincott Company. 1895. Last Accessed 6/25/2018. http://www.archive.org/stream/manualofelementa00atwarich#page/24/mode/1up/search/conclusion. Buy the book
3. Duncan, William H.. The Elements of Logic. pg 8. www.archive.org. Whiting, Backus & Whiting. 1804. Last Accessed 6/25/2018. http://www.archive.org/stream/elementsoflogici00dunc#page/8/mode/1up/search/conclusion. Buy the book

McAdams, David E. Conclusion. 4/16/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/conclusion.html.

### Revision History

4/16/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)