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I am teaching a Linear Algebra class for first year students and one problem we are discussing in class is the fact that the sum of all elements in a finite field $F$ is $0$ if $|F|>2$. This result is not true in $\mathbb F_2$, a colloquial explanation would be that there is not enough "space" in $\mathbb F_2$.

What are some other nice and interesting examples of theorems that are true except for "small" values or boundary cases? (basic or advanced, from any area of maths, ...)

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    $\begingroup$ Cf. law of small numbers $\endgroup$
    – J. W. Tanner
    Oct 26, 2021 at 21:06
  • $\begingroup$ Try proving $1\not= 0$ in a (unitial) ring, except for one small example. Then explain why that case is not considered a field $\endgroup$
    – Henry
    Oct 26, 2021 at 21:06
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    $\begingroup$ Some examples are listed here, here and here. $\endgroup$
    – pregunton
    Oct 31, 2021 at 7:48

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