Hguy

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Hello, Hguy, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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Please remember to sign your messages on talk pages by typing four tildes (~~~~); this will automatically insert your username and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question on this page and then place {{help me}} before the question. Again, welcome! Dmcq (talk) 21:26, 11 February 2013 (UTC)

Why I changed "x cubed =1" section in Mathematical fallacy: http://en.wikipedia.org/wiki/Mathematical_fallacy

First off, the reason I changed original section was NOT because it is incorrect. After all, there is not a correct way to show 3=0.

The reason I changed it is because the original statement of the problem, as well as the explanation, does not properly convey the main idea that the fallacy intended to convey. There are a few objectionable points in the original post:

1. The first statement, "assuming the following equation for a real x", is already wrong, because $x^{2}+x+1=0$ has no real solution. A fallacy problem normally starts with a correct statement. As the original section was written, the fallacy is the first statement: the assumption that $x$ is a real solution to $x^{2}+x+1=0$, and the rest of the proof is actually completely correct. The wrong conclusion of 3=0 is caused by the wrong initial assumption. In that case, one might as well start the problem by saying let 3 = 0, but I don't think this is what the article is intended.

2. In the statement of the fallacy in the original post, it states that $x=1$ is the only real solution to $x^{3}=1$, which is true, but it never provides a proof of that in the article. In other words, the explanation itself lacks solid justification. If one wants to prove that $x^{3}=1$ has no other real solutions except $x=1$, one would probably have proved that $x^{2}+x+1=0$ has no real solution, which is to say that the very first assumption is incorrect anyways, and defeats the purpose.

3. The title of the section, x cubed = 1, does not really reflect the heart of the issue. The issue demonstrated in this fallacy is not really specific to cubic root. One could use the exact similar reasoning as in the original post, to come up with a problem not involving cubic root. Start with assuming $x$ is a solution of $x=-1$, and then derive that $x$ must satisfy $x^{2}=1$, and hence $x=1$, and hence $1=-1$. So there is nothing special about cubic root in the reasoning of the original post.

What the original post wants to convey is that it is WRONG to conclude $x=1$ from $x^{3}=1$. So the real fallacy the original post intends to convey is extraneous solutions:

let x be a solution of EQ1, and then we derive that x satisfies EQ2. Then find a solution to EQ2 and conclude that it is also a solution of EQ1.

Above is really the fallacy to the spirit of the original post.

Therefore, my changes to the statement of the problem, and my explanation are to exactly convey this idea, and I believe that my change to the section provides a better service to the readers of the section than the original post.Hguy (talk) 22:12, 9 February 2013 (UTC)

Mathematical fallacy

It is usual to put reasons onto the talk page of an article as at Talk:Mathematical fallacy#Uncited content. Content needs WP:Verifiability and this article in particular needs verifiability to stop people sticking in their own thoughts as you describe above. Dmcq (talk) 21:25, 11 February 2013 (UTC)

Please read WP:Verifiability. Another article in Wikipedia does not provide that, and especially not one that has a warning that it is missing any references. Dmcq (talk) 08:40, 12 February 2013 (UTC)