Prove that a set in $\mathbb R^3$ is not an algebraic set
Let $X=(cos(t),sin(t),t)$ Consider the plan $P$ defined by $(x,y,z): x=0$, $X\cap P=(0,(-1)^k,\pi/2+k\pi), k\in Z$ is not algebraic, thus $X$ is not algebraic.
Prove that a set in $\mathbb R^3$ is not an algebraic set
Let $X=(cos(t),sin(t),t)$ Consider the plan $P$ defined by $(x,y,z): x=0$, $X\cap P=(0,(-1)^k,\pi/2+k\pi), k\in Z$ is not algebraic, thus $X$ is not algebraic.