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1) the metric is a bilinear form on a space

2) the metric tensor is basically the same thing

Is this correct?

If so, how is the metric related to/different from the distance function in that space?

Some other sources state that the metric is defined as the distance function. This is where I'm getting confused.

With reference to SR, should i consider the Space-Time interval as the metric, or the metric tensor denoted as g?

I don't know if I'm being able to communicate efficiently, though. :uhh: