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Proof / Disclaimer With Example

I think my post is a bit long and a lot of hassle lately. Today I will make a basic article. This is for website refreshment as well. Happy reading.

Most people use the equivalent method to prove mathematical statements. Even to prove the error of a statement. Though there are other ways to prove error statement, ie with an example of denial. This is considered sufficient because a statement must be perfect. Also because the truth must be perfect in mathematics.

Suppose there is a statement “If n\in\mathbb{N} then n^{2}+n+1 is prime”. Suppose we want to deny the statement. We have a presumption that n^{2}+n+1 not always prime. Then simply indicated there is a number n=k such that k^{2}+k+1 is not prime. For this case, we take n=4 then n^{2}+n+1=4^{2}+4+1=21 is not prime. This example is sufficient to prove that the above statement is false.

Thanks for reading.

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