# A generic curve

Exhibit a curve in $\Bbb{R}^n$ such that any $(n+1)$-uple of points in its trace is in general position.

1. $x \mapsto (1,x,x^2,\ldots,x^{n-1})$. Since the Vandermonde matrix is invertible when evaluated at distinct points the result follows. For the case $n=1$ use the identity.