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form the basis on which all of modern mathematics is to be constructed.

Basic terminology

In modern usage, a definition is something, typically expressed in words, that attaches a meaning to a word or group of words. The word or group of words that is to be defined is called the definiendum, and the word, group of words, or action that defines it is called the definiens. For example, in the definition "An elephant is a large gray animal native to Asia and Africa", the word "elephant" is the definiendum, and everything after the

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