Meaning of the word "hopeless"

hopeless
certain to fail
[adjective]
Examples:
the situation is hopeless
(informal to emphasize how bad it is) beyond hope of management or reform
[adjective]
Examples:
she handed me a hopeless jumble of papers
he is a hopeless romantic
of a person unable to do something skillfully
[adjective]
Examples:
I'm hopeless at mathematics
without hope because there seems to be no possibility of comfort or success
[adjective]
Examples:
in an agony of hopeless grief
with a hopeless sigh he sat down