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A comment on Functions are Vectors.
f + g = g + f
f + (g + h) = (f + g) + h
f + -f = 0
(a * b) * f = a * bf
a (f + g) = af + ag
(a + b) * f = af + bf
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f + g = g + f
f + (g + h) = (f + g) + h
f + -f = 0
(a * b) * f = a * bf
a (f + g) = af + ag
(a + b) * f = af + bf