Contrived Proof
A problem posed by T. Hewitt, London:
Ye learned in numbers, how will you contrive
To prove that Nothing is equal to five?
Solution: Find the error's in the Hewitt's proposed answer: “Put a = 1 and n = 5+1 = 6, that is one more than the given number, then the following work will clear this matter: (1an)/(1a) = 1 = a + a^{2} + a^{3} + a^{4} + &c. to an^{1} = (1a^{6})/(1a) = 1 + a + a^{2} + a^{3} + a^{4} = (11^{6})/(11) + (11)/(11) = 1 only because the numerator and denominator are equal. Then will a + a^{2} + a^{3} + a^{4} + a^{5} = 5 be also = 0.” Or, is there no error in this response?
Source: The Gentleman’s Mathematical Companion, 1797
