Proof by induction: Tube carriages are infinitely large
Take a standard Northern Line Tube carriage.
However many people are on board that carriage, at least one more adult can squeeze on. This step has been proven at every station on the northbound southern leg of the Northern Line for many a year.
The smallest adult weighs 4.5kg, and with the average human having a body density of around one gram per cubic centimetre, that equates to a lower bound of 0.0045 cubic metries occupied by a person.
Therefore the lower bound for the volume taken up by a Northern Line Tube carriage is 0.0045 cubic metres multiplied by the number of occupants.
Given that the number of occupants can always be increased by one, a Northern Line Tube carriage is infinitely large.