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I stopped agreeing when reading nr 7. Einsteins notation (X_n Y^n being defined as sum over ‘n’ of X_n times Y^n) is one of the most elegant and simple solutions that really work.

If if you need x_n = y_n * z_n, you would write just that. Only when you write y_n * z^n would the notation imply summation over n.

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> Einsteins notation (X_n Y^n being defined as sum over ‘n’ of X_n times Y^n) is one of the most elegant and simple solutions that really work.

Yes, but that notation still includes the indexes being summed over, which I think is the point that no. 7 was trying to make. What doesn't work is a notation that just says XY, without any indexes whatsoever. The ordering of indexes and the specification of which indexes are being summed over matters, so a notation that leaves those things out doesn't work.

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