The Paradox
Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms.
Read more about this topic: Hilbert's Paradox Of The Grand Hotel
Famous quotes containing the word paradox:
“A good aphorism is too hard for the teeth of time and is not eaten up by all the centuries, even though it serves as food for every age: hence it is the greatest paradox in literature, the imperishable in the midst of change, the nourishment which—like salt—is always prized, but which never loses its savor as salt does.”
—Friedrich Nietzsche (1844–1900)
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)