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Giuseppe Peano Quotes
1858–1932 Italy
Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician, logician, and one of the founders of modern mathematical logic and set theory. His work, summarized in Formulario mathematico (1895) was highly influential and the standard Peano axioms of the natural numbers are named in his honor.
Italy Linguists Mathematicians Philosophers Also known as: Peano
Random Giuseppe Peano quote
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Any property belonging to 0 and to the immediate successor of any number that also has that property belongs to all numbers.
As expressed in Galileo's Finger: The Ten Great Ideas of Science (2003)
0 is not the immediate successor of any number.
As expressed in Galileo's Finger: The Ten Great Ideas of Science (2003)
All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers.
Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses.
Sui fondamenti della geometria (1894)
Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.
Geometric Calculus (1895)
Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.
In every science, after having analysed 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 the science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction.
Notations de Logique Mathématique (1894)