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Address comments from #44
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chiphogg committed Oct 15, 2023
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Expand Up @@ -11,7 +11,7 @@ author:
email: <[email protected]>
- name: Johel Ernesto Guerrero Peña
email: <[email protected]>
- name: Charles Hogg
- name: Chip Hogg
email: <[email protected]>
- name: Nicolas Holthaus
email: <[email protected]>
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15 changes: 8 additions & 7 deletions src/2982R0_std_quantity_as_a_numeric_type.md
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Expand Up @@ -1002,10 +1002,10 @@ number. For example, the ratio between one foot and one inch is 12.
### Unit magnitudes

In principle, this scaling factor can be any positive real number. In mp-units and Au, we have used the term
"magnitude" to refer to this scaling factor. (This should not be confused with the logarithmic "magnitude"
unit commonly used in astronomy.)
"magnitude" to refer to this scaling factor. (This should not be confused with other uses of the term, such
as the logarithmic "magnitude" unit commonly used in astronomy.)

In the library implementation, each unit is associated with a magnitude. However, for most units the
In the library implementation, each unit is associated with a magnitude. However, for most units, the
magnitude is a fully encapsulated implementation detail, not a user-facing value.

This is because the notion of "the" magnitude of a unit is not generally meaningful: it has no physically
Expand All @@ -1016,10 +1016,11 @@ assign any magnitude $m_s$ to the second, because it's an independent dimension
choice, it fixes the magnitude for derived units, and we must assign, say, $(5280 m_f) / (3600 m_s)$ to the
_mile per hour_.

The one exception to the arbitrariness of magnitudes is _dimensionless_ units. Because their dimension is
null, quantities of these units can be meaningfully compared to their squares and other powers. For example,
the magnitude of _percent_ is $1 / 100$, and the magnitude of _squared percent_ (or _pertenk_, "per-10-k") is
$1 / 10000$. We cannot choose another value for the magnitude without producing observably incorrect results.
The one exception to the arbitrariness of magnitudes is _dimensionless_ units. Because their dimension is the
identity, quantities of these units can be meaningfully compared to their squares and other powers. For
example, the magnitude of _percent_ is $1 / 100$, and the magnitude of _squared percent_ (or _pertenk_,
"per-10-k") is $1 / 10000$. We cannot choose another value for the magnitude without producing observably
incorrect results.

### Requirements and Representation

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