"Certainly the statement 2 x (1/2) = 1 is arithmetically correct. But do two half-sheets of paper make one whole sheet and do two half-shoes make one whole shoe? Clearly two physical halves never make one whole unless they can be joined in such a way that the halves merge into one whole. Two half-dollars, in general, equal one whole dollar in purchasing power, but in areas where silver is preferred to bills two half-dollars are worth more. To know whether the arithmetic is applicable, we must examine the physical situation."
- Morris Kline in Mathematics for the Non-mathematician