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S is very special and it is called the strong composition combinator, because when applied to two functions, let us say, f and g, as well as x, then the resulting term gx (fx) expresses the composition of g and f both applied to the same argument x.

Now we can define a metric tensor, g, on our manifold: The metric tensor assigns a metric, gx, to every point x in the manifold (such that it varies smoothly with x in the manifold).
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

Now, a metric at our point x is a function gx (Xx, Yx), which takes in the two tangent vectors Xx and Yx (at x), and outputs a real number.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

Now we can define a metric tensor, g, on our manifold: The metric tensor assigns a metric, gx, to every point x in the manifold (such that it varies smoothly with x in the manifold).
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

Now, a metric at our point x is a function gx (Xx, Yx), which takes in the two tangent vectors Xx and Yx (at x), and outputs a real number.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

Thus we arrive at a direct contradiction, since the state of S2 postmeasurement cannot be both gx  and one of gy  or gy+.

And with the lack of diacritics available on most keyboards, it does not always even meetin practicethe claim of "one letter, one sound"eg., gx or gh.

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O ax bx cx dx ex fx gx hx ix jx kx lx mx nx ox px qx rx sx tx ux vx wx xx yx zx

Yxu've gxt tx gx, yxu knxw, sx gx at xnce, and dxn't gx slxw; fxr nxbxdy xwns yxu here, yxu knxw.
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