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Meanings of choose arbitrarily in English

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Usage of choose arbitrarily in English
1
Thus (G) may be chosen arbitrarily, and also parts of (P); all these laws are conventions.
Sidelights on Relativity
2
These book-marks cannot be chosen arbitrarily.
A Library Primer
3
These sections have been chosen arbitrarily, i.e., {1}, {2}
The Pilgrim's Progress from this world to that which is to come ...
4
The point A was chosen arbitrarily, but it is evident that that of the needles depends on its distance from the point of convergence.
Scientific American Supplement, No. 363, December 16, 1882