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You know how $2+2 =4$, $2\times 2 = 4$ and also $2^2 = 4$? What is the mathematical term for that when a number can have many operations and the same answer? And are there any other numbers with that situation, like $1$, because $1 \times 1 = 1$, $1 \div 1 = 1$, $1^2 = 1$. And obviously $0$.

So can you please answer this question

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  • $\begingroup$ To the best of my knowledge there isn't one. Why should there be a mathematical term? $\endgroup$ – Clive Newstead Jan 14 '14 at 0:43
  • $\begingroup$ I'm not really sure what pattern you're getting at since the ones for 2 and 1 you described are different. $2/2 \neq 4$ and $1+1 \neq 1$. $\endgroup$ – Jemmy Jan 14 '14 at 0:44
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    $\begingroup$ I believe such occurrences are typically called coincidences. $\endgroup$ – Cameron Buie Jan 14 '14 at 0:49
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    $\begingroup$ Some people call them Karl käfer equations $\endgroup$ – user88576 Jan 14 '14 at 0:52
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    $\begingroup$ There are lots of modular solutions, e.g. $\rm\, mod\ 4n\!:\ 2n+2n \equiv 2n * 2n \equiv (2n)^{2n} \equiv 0,\,$ for example $\rm\, mod\ 100\!:\ 50+50\equiv 50*50\equiv 50^{50}$ $\endgroup$ – Bill Dubuque Jan 14 '14 at 1:01
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Solving for the proposed relations:

$x+x = y$

$x^2 = y = 2x$

So the only numbers are $2$ and $0$, but $0^0$ is not $0$, hence the only number with this property is called two.

Now, for the second one, $x/x$ is always $1$.

There is no mathematical term for numbers being the result of interesting operations. In fact it can be proved that every number is interesting in some sense. If you're interested in number patterns, take a look at http://oeis.org/

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