I am attaching a picture of a proof from the book "general relativity" by wald. This is supposed to show that the tangent space of an n dimensional manifold is also n dimensional. I have two questions.(adsbygoogle = window.adsbygoogle || []).push({});

In equation 2.2.3 couldn't the function be anything at a since the (x-a) term is 0?

How is the equality in equation 2.2.5 justified, I'm just not seeing it

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof of dimension of the tangent space

**Physics Forums | Science Articles, Homework Help, Discussion**