# question on complete vector fields

Could any one help me to solve these two problems on vector fields

1. Any $\mathbb{C}^{\infty}$ vector field on a compact manifold is complete.

2. Is every vector field on $\mathbb{R}$ complete?

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The 1st is true, not the 2nd. The flow associated to $\dot{x}=x^2$ is given by $\phi_t(x)=x/(1-tx)$, and obviously does not exist for every $t$.