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Zero Zero is the Cardinal Number of the Empty Set It’s the number of things you have when you don’t have anything It’s the most effective computing device every invented Without it we could not distinguish 23 from 20030 or 20300 or 23000 and arithmetic would be a good deal tougher than it is And now look at this Addition 2 + 0 = 2 3+0=3 4 + 0 = 4 and so on Multiplication 2 1 = 2 3 1=3 4 1 = 4 and so on 0 does the same thing for addition that 1 does for multiplication Sign in Boston’s Museum of Science " ! #$ ! " %! &! " ' ! ( )* “In 628, in Brahmasphutrasiddhanta, Brahmagupta defined zero as the result of the subtraction of a number from itself (a – a = 0) and described its properties in the following terms” (Ifrah p. 439) “When zero (shûnya) is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.” Moreover using terms like fortune (dhana), debt (rina) to express positive and negative numbers Brahmagupta wrote “A debt minus zero is a debt A fortune minus zero is a fortune Zero (shûnya) minus zero is nothing (kha) A debt subtracted from zero is a fortune So a fortune subtract from zero is a debt The product of zero multiplied by a debt or a fortune is zero The product of zero multiplied by itself is nothing.” Wood-Block Engraving by Gregorius Reisch 1503 Lady Arithmetic smiling on the algorist (on the left) working with Arabic (Indian) Numbers # $ -. / %& ' + , / 0 ! '( ) ' *** %& ' + , -. / / (/ 1 ' ( ) ' **+ , %-' 0/ 2& 0 . / / 3 /' /'. / '+000 1 % '2 3 4/ 1 / 5 / ' $ ' ***