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Saturday, August 25, 2018

Giuseppe Peano and zero


Photo source: Wikimedia Commons


Giuseppe Peano (1858-1932) was an Italian mathematician best known for his contributions to set theory and the axiomatization of natural numbers. Mathematician Ugo Cassina said,


"Peano - whether in Logic or in Mathematics - never worked with pure symbolism - he always required that the primitive symbols introduced represent intuitive ideas to be explained with ordinary language." (Quoted in The Mathematical Philosophy of Giuseppe Peano by Hubert Kennedy, 1963)


Mathematician Gregory H. Moore said,


"Bertrand Russell never wavered in acknowledging his intellectual debt to Giuseppe Peano. In many ways the contribution that Russell made to the foundations of mathematics, culminating in Principia Mathematica, strongly bears Peano's mark." (1980)


The rest of this post is some quotes from Peano.




"No number before zero. The numbers may go on forever, but like the cosmos, they have a beginning." (


"1. Zero is a number. 2. The immediate successor of any number is also a number. 3. Zero is not the immediate successor of any number. 4. No two numbers have the same immediate successor. 5. Any property belonging to 0 and to the immediate successor of any number that also has that property belongs to all numbers." (Quoted in The Mathematical Philosophy of Giuseppe Peano by Hubert Kennedy, 1963)


"In every science, after having analyzed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that cannot be reduced among them, and that one can define no further. These are the primitive ideas of science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction." (Notations de Logique Mathematique, 1894)