beliebig
any / arbitrary
Any one; without a specific rule or selection. It describes that the choice is free and arbitrary.
Wählen Sie eine beliebige Zahl zwischen eins und zehn.
Choose any number between one and ten.

any / arbitrary
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any / arbitrary
Any one; without a specific rule or selection. It describes that the choice is free and arbitrary.
Wählen Sie eine beliebige Zahl zwischen eins und zehn.
Choose any number between one and ten.

The adjective 'beliebig' (any/arbitrary/generic) is related to the verb 'belieben' (to please, to wish). Something is 'beliebig' when you can choose it freely 'nach eigenem Belieben' (according to your own preference), that is, according to your own wishes.
Sie können die Zutaten für den Salat nach Belieben variieren.
You can vary the ingredients for the salad as you like.
'Beliebig' is very often used to modify adverbs like 'oft' (often), 'lange' (long), or 'viel' (much/a lot). It expresses that the frequency, duration, or amount is unlimited or freely selectable.
Mit dieser Software können Sie das Dokument beliebig oft kopieren.
With this software, you can copy the document as often as you like.
The negative meaning 'interchangeable' can be recognized from context. It is often used in reviews of art, design, or music to express that something has no personality or originality of its own.
Seine neueste Musik klingt professionell produziert, aber leider auch völlig beliebig.
His latest music sounds professionally produced, but unfortunately also completely generic.
In its neutral meaning, 'beliebig' is often used in instructions or technical contexts. Typical combinations are 'eine beliebige Zahl' (any number), 'ein beliebiger Zeitpunkt' (any point in time), or 'in beliebiger Reihenfolge' (in any order).
Die Teilnehmer können die Aufgaben in beliebiger Reihenfolge bearbeiten.
The participants can work on the tasks in any order.
especially / special
'besonders' and 'beliebig' are clear opposites here. 'besonders' says that something is not normal or not everyday. It makes something stand out. 'beliebig', on the other hand, says that something can simply be any one, or seems interchangeable. If something is 'besonders', it has a special value or a feature of its own. If something is 'beliebig', the exact choice is usually not important.

Für die Übung könnt ihr ein beliebiges Thema wählen.
For the exercise, you can choose any topic.
Für die Bewerbung sucht der Chef einen besonders passenden Lebenslauf aus.
For the application, the boss selects a particularly suitable résumé.