A special case of: checking if a vector $v$ in a finite dimensional vector space over the reals is linearly independent of a set of vectors $\{u_i\}$.
(almost equivalently: checking equality (in the sense of extensionality) of $k\geq 2$ bounded integer-valued functions. the output of such functions can be written as real numbers in $[0,1]$, but you have to have to pad each integer so that you don't accidentally call two different outputs the same real number (due to $0.99\ldots = 1.00$ etc). How to solve the halting problem: have a function $f(n) = 1$. Given some arbitrary program/function, nest it in a function $g(n)$ which runs it for $n$ cycles, and outputs $1$ if it halted, $0$ otherwise. $f$ and $g$ are equivalent iff the program does not halt.)