BvU said:
Note that there are some complications in dimensionless units
That was in november 2020. The fluid nature of Wikipedia makes the links completely worthless and confusing.
I know next to nothing about the inner workings of Wikipedia, but I can see that there have been numerous edits since then.
Since I find this an intriguing subject: Plodding through the edits one actually can dig up the whole drama (kudos to Wikipedia on that one!) Sorry to rant on and on but here goes:
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New text (or better: currect text)
Wikipedia said:
As the ratio of two lengths, the radian is a
pure number. In fact, the radian is defined as 1.
[4]
Still with a reference to ISO 80000-3:2006

?!?
[
reference ISO 80000-3:2006 is outdated and withdrawn. Now ISO 80000-3:2019 (-- probably identical for this topic--)
]
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Old text
The radian is defined as 1. ##\qquad]##
[reference ISO 80000-3:2006
]
There is controversy as to whether it is satisfactory in the
SI to consider angles to be dimensionless.
[
(there seem to be multiple links to the same stuff)
]
This can lead to confusion when considering the units for frequency and the Planck constant.
[4][7]
[
]
[
]
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These changes are dated January 23 , 2021. No more controversy.
Integrity of post #5 restored, I hope. Phew...
In short: the radian is a unit with a special name for a derived quantity that has dimension m/m
To boot: all this fuss about complications has nothing to do with the confusion of the OP
But the problems of
@BobF remain. Introducing am/m renders a Taylor series for a sine illegal
##\ ##