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While researching I have found two definitions for element.

First, elements are pure substances that consist only one type of atoms. According to this O2, O3, Diamond and in short all allotropes are elements. This seems counter- intuitive to me.

Second, Elements are pure substances whose particles cannot be broken down to simpler substances by chemical reactions. According to my understanding, this definition signifies that substances of periodic table are elements. Thus, allotropes are not elements.

Also, are isotopes of elements considered element ?

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    $\begingroup$ chemical element doi.org/10.1351/goldbook.C01022 (1) A species of atoms; all atoms with the same number of protons in the atomic nucleus. (2) A pure chemical substance composed of atoms with the same number of protons in the atomic nucleus. Sometimes this concept is called the elementary substance as distinct from the chemical element as defined under 1, but mostly the term chemical element is used for both concepts. $\endgroup$
    – Martin - マーチン ♦
    Commented Jun 23 at 19:59
  • $\begingroup$ Take all meanings of the term chemical element and then decide which of them fit the case and which do not. $\endgroup$
    – Poutnik
    Commented Jun 24 at 4:46

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The definitions you provide were good enough for 18-19th centuries. Unfortunately, many school books in different parts of world have not changed. The modern understanding of an element is that its nucleus has the same number of protons (Z). An element is identified by its atomic number not by anything else. Element can exist as single atoms, like $\ce{He}$, or in molecular form $\ce{O3}$, $\ce{C60}$ and $\ce{S8}$. They are all elements.

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