I know that αδύνατος can also mean weak, but with this phrase is clearly not the case. That being said, and referring to 'weakness', what is the difference between 'αδύνατος' and 'αδύναμος'?
Hi Vasilis, not as a noun.
Impossible = αδύνατον as an adjective and it can be only neutral.
E.g. Είναι αδύνατο(ν) (impersonal verbal expression) = It is impossible
Είναι αδύνατος/αδύνατο (noun) = He is thin/It is thin (as neutral noun, e.g. when referring to an animal)
Same for δυνατός. (e.g. Είναι δυνατόν is different from Είναι δυνατός/είναι δυνατό)
Impossible is not always neutral. You can also say for example "Αυτός ο συνδυασμός είναι αδύνατος" meaning "this combination is impossible". So "impossible" is αδύνατος, -η, -ο(ν).
Αδύνατος comes from the ancient greek word "δυνατός" which means powerful with the α- in the beginning showing lack of. So α-δύνατος means someone without power or something that is impossible to happen or thin (see https://el.wiktionary.org/wiki/%CE%B1%CE%B4%CF%8D%CE%BD%CE%B1%CF%84%CE%BF%CF%82)
But we also say "Αυτός ο κωδικός είναι αδύναμος" meaning "this password is weak".
Αδύναμος comes from the ancient Greek word "δύναμις" which means power and the α- in the begining showing lack of. So α-δύναμος means someone without power (physical, constitutional, fianancial, e.t.c.) or in other words weak. (see https://el.wiktionary.org/wiki/%CE%B1%CE%B4%CF%8D%CE%BD%CE%B1%CE%BC%CE%BF%CF%82)
So we say:
"Νιώθει αδύναμος από την αρρώστια" = he feels weak due to illness.
"Είναι αδύνατος από την αρρώστια" = He is thin because of the illness. (αδυνατίζω = I lose weight)
"Ο συνδυασμός είναι αδύναμος". = The combination is weak.
"Ο συνδυασμός είναι αδύνατος" = The combination is impossible.