Am I Calculating the Riemann Tensor Correctly?

[help1please]

See, I was always taught a certain order to multiply out brackets.

This is what I do, the dashes represents the order of multiplication this time:

(a'+b)(c'+d)

(a'+b)(c+d')

(a+b')(c'+d)

(a+b')(c+d')

This is what susskind does:

(a'+b)(c'+d)

the terms cancel. Naturally.

Then for only the RHS (where the minus indicates to different sides) ---*** its this bit I don't agree with because of my own order.

(a+b')(c'+d)

then for the left he does

(a'+b)(c+d')

Which is not the kind of order I am used to. Then he goes on to multiply the last lot out like I would

(a+b')(c+d')

 

[clamtrox]

Well, like I said earlier, summation commutes, so you just need to get used to people writing down their sums in different order...

 

[help1please]

Well, like I said earlier, summation commutes, so you just need to get used to people writing down their sums in different order...

Can you give me an example please, like show me the math written out where the summation is commuting all over the place. I have used the notation

A_{[\mu}B_{\nu]} before, just never seen it in its full form. How would these indices commute, thank you.

 

[help1please]

The fact susskind has not done this has only caused more confusion for me, for anyone I'd presume that would like to follow the math...

 

[clamtrox]

For example, 1+2=2+1=3. This is what commuting means.