# What is this math term called?

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 $0$.

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

$x+x = y$
$x^2 = y = 2x$
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 $1$.