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I am unsure about what is the correct (english) word to use in solving linear systems. To be more specific, here is a good example. Suppose to solve the following linear system of equations:

$\begin{cases} x+y+z=0\\ -x+2z=0 \end{cases}$

Since these are two non parallel planes, they intersect in a straight line, so the system has $\infty^1$ solutions. My question is about that $\infty$: is it infinity to the power of one or is it infinite to the power of one?

If this is not the appropriate setting for this type of question, I apologize.

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  • $\begingroup$ @SalmonKiller My uncertainty comes from the way it is said in Italian language because $\infty^1$ is used as an adjective that qualifies the number of solutions, so it should be infinite to the power of one, but to me it does not sound right because I look at it as the cardinality of the set of solutions. Infinity sounds more appropriate. $\endgroup$ – Nadia Sep 20 '18 at 19:56
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I'm pretty sure you say infinity to the power of one since that's the noun. I would say however that's an infinite line, plane, or if it's multi-dimensional I think it's better today it's a 4-dimensional infinite plane or something of this sort.

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