Gottlob Frege and Natural number

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Difference between Gottlob Frege and Natural number

Gottlob Frege vs. Natural number

Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

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Axiomatic system

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

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Constructivism (mathematics)

In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.

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Finitism

Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects.

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Foundations of mathematics

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.

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Giuseppe Peano

Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist.

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Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Russell's paradox

In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.

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Set-theoretic definition of natural numbers

Several ways have been proposed to construct the natural numbers using set theory.

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