A story about Prof. De-Morgan

Prof. Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous.

Beyond his great mathematical legacy, the headquarters of the London Mathematical Society is called De Morgan House and the student society of the Mathematics Department of University College London is called the August De Morgan Society.

De Morgan proceeds to give an inventory of the fundamental symbols of algebra, and also an inventory of the laws of algebra. The symbols are 0, 1, +, −, ×, ÷, ()⁽⁾, and letters; these only, all others are derived. His inventory of the fundamental laws is expressed under fourteen heads, but some of them are merely definitions. The laws proper may be reduced to the following, which, as he admits, are not all independent of one another:

1.     Law of signs. + + = +, + − = −, − + = −, − − = +, × × = ×, × ÷ = ÷, ÷ × = ÷, ÷ ÷ = ×.

2.     Commutative law. a+b = b+a, ab=ba.

3.     Distributive law. a(b+c) = ab+ac.

4.     Index laws. a^b×a^c=a^b+c, (a^b)^c=a^bc, (ab)^d= a^d×b^d.

5.     a−a=0, a÷a=1.