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An affine space is a tuple (π, π©) where π© is a vector space and π has the same structure as π© but has "forgotten its origin"; ie. unlike a vector space, ha
by Sharlin 3y ago
An affine space is a tuple (π, π©) where π© is a vector space and π has the same structure as π© but has "forgotten its origin"; ie. unlike a vector space, has no privileged zero point. As such, multiplication by a scalar is not meaningful, and neither is the addition of two elements of π. The elements of π are called points, and the elements of π© are translation vectors, or simply translations. The fundamental operations are:
(β): π Γ π β π© β gives the translation from a point to another point, and
(+): π Γ π© β π β applies a translation to a point.
(For convenience we can also write π β π = π + βπ for all π β π, π β π©).
The Celsius and Fahrenheit scales are affine, and technically should have separate units for temperatures and temperature differences so that mishaps like in TFA would be less likely to happen.