1-manifold is orientable I am trying to classify all compact 1-manifolds. I believe I can do it once I can show every 1-manifold is orientable. I have tried to show prove this a bunch of ways, but I can't get anywhere.
Please help,
Note, I am NOT assuming that I already know the only such manifolds are [0,1] or $S^1$. This is my end goal.  

There are only two connected, compact 1-manifolds up to homeomorphism.  These are $[0,1]$ and $\mathbb{S}^1$ (the circle).  These will (very likely) be trivially orientable given your definition of orientability.
