"Strong typing vs. strong testing"
tfb at tfeb.org
Tue Oct 12 14:23:11 CEST 2010
On 2010-10-12 11:16:09 +0100, Ben said:
> Angles aren't "true" units, as they are ratios of two lengths. They
> are more of a "pseudo" unit.
That's right, in fact angles are pure numbers. In general any function
which raises its argument to more than one power (for instance anything
with a non-trivial power series (Taylor series) expansion) doesn't make
much sense if its argument has units. Transcendendal functions are all
like that, of course.
For instance sin(x) = x + s^3/6 + O(x^5), so sin(1m) would be 1m +
1m^3/6 + O(m^5), and it doesn't make sense to add metres and cubic
metres (let alone the infinite number of higher-order terms!).
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