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:
“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)
“When a paradox is widely believed, it is no longer recognized as a paradox.”
—Mason Cooley (b. 1927)