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I saw the Cayley-Hamilton theorem

Let $\mathbf{A}$ be a $n\times n$-matrix, and $p(\lambda)=\det(\lambda \mathbf{I}_n-\mathbf{A})$ the characteristic polynomial of $\mathbf{A}$. Then $p(\mathbf{A})=\mathbf{0}$

and I thought it was trivial since $\det(\mathbf{A}-\mathbf{A})=0$. I checked with Wikipedia and learned that this didn't work because $\lambda$ is a scalar, and $\det(\mathbf{0})$ is also a scalar, and not a matrix. This brings me to my question:

Are there any other results that seem trivial, but aren't?

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marked as duplicate by user334732, Arnaud D., Community Apr 10 '18 at 9:52

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The Jordan curve theorem states that, if you draw a closed non-intersecting curve in the plane, it divides the plane into those points that are inside the curve, outside it or on it.

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The weak Goldbach conjecture (a theorem now, it seems, proved by Harald Helfgott): Every odd integer $n>5$ is a sum of three primes. If you try yourself examples, this seems trivially true. There are millions of possibilities for a big odd $n$. Nevertheless, the proof is extremely complicated.

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    $\begingroup$ In case anyone doesn't know, it was proved in 2013 by Harald Helfgott. (I looked it up because I didn't realise it had even been proven.) $\endgroup$ – J.G. Apr 9 '18 at 16:47
  • $\begingroup$ Yes, there are $5$ arXiv papers, see wikipedia. However, an article with a proof has not been published in a journal yet. $\endgroup$ – Dietrich Burde Apr 9 '18 at 18:05

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