[thanatropism]

> Programming languages aren't able to express arbitrary real numbers,

No system of finite representations is able to express arbitrary real numbers.

[quickthrower2]

Depends what you mean by an arbitrary real number. Any constructed real number could be stored as it’s construction steps. Eg use a series for Pi.

But paradoxically you can store “any” real number, eg the number made up of all future lottery draws.