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0 and Peano axioms

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between 0 and Peano axioms

0 vs. Peano axioms

0 (zero) is both a number and the numerical digit used to represent that number in numerals. In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

Similarities between 0 and Peano axioms

0 and Peano axioms have 15 things in common (in Unionpedia): Absorbing element, Category (mathematics), Category theory, Computable function, Empty set, Greatest and least elements, Identity element, Initial and terminal objects, Integer, Natural number, Number theory, Oxford University Press, Princeton University Press, Set theory, Well-order.

Absorbing element

In mathematics, an absorbing element is a special type of element of a set with respect to a binary operation on that set.

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Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.

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Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

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Computable function

Computable functions are the basic objects of study in computability theory.

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Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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Greatest and least elements

In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S that is greater than every other element of S. The term least element is defined dually, that is, it is an element of S that is smaller than every other element of S. Formally, given a partially ordered set (P, ≤), an element g of a subset S of P is the greatest element of S if Hence, the greatest element of S is an upper bound of S that is contained within this subset.

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Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

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Initial and terminal objects

In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Natural number

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").

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Well-order

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.

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The list above answers the following questions

0 and Peano axioms Comparison

0 has 268 relations, while Peano axioms has 129. As they have in common 15, the Jaccard index is 3.78% = 15 / (268 + 129).

References

This article shows the relationship between 0 and Peano axioms. To access each article from which the information was extracted, please visit:

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