The phrase "actually arbitrary" is correct and usable in written English.
It can be used to emphasize that something is not determined by any specific rules or criteria, often in a context where one might expect it to be otherwise.
Example: "The choice of colors for the project was actually arbitrary, as there were no guidelines provided."
Alternatives: "truly random" or "genuinely without reason".
The numbers are actually completely arbitrary (it could be -6.432 instead of -5), only the order of numbers (-25 is less than -5) matters.
Observe that is actually an arbitrary point on the curve, which represents one of two equilibrium curves for system (1.1).
Then I may actually sign some arbitrary sense of such.
But Dr Hager says this is actually a pretty arbitrary goal, based on a single study carried out in Japan 50 years ago.
I actually had one arbitrary rule that there was no purple allowed and we tried to use as much green and blue -- which goes back to that girl/boy thing -- as we could.
The results strongly depend on the value for the parameter q x, r) (the probability that an inhibitor actually inhibits an arbitrary reaction).
We also show that through verification, we can actually check whether an arbitrary action theory maintains boundedness.
Once the shock of the new had worn off, I began to understand that this short list, apparently strange and arbitrary, was actually very good indeed.
There is a lively debate among social scientists about whether increased virtual communication — stretching across space and making distance seem almost arbitrary — has actually brought families closer, especially those with festering emotional wounds or ongoing feuds.
These qualities, although they may look almost arbitrary, are actually deeply related, practically different facets of the same underlying idea.
Whatever Russia does on the world stage, no matter how seemingly aggressive or arbitrary, is actually in self-defense against an implacable enemy.
