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"For the next generation"
© 2025 Astra.si. All rights reserved.
"For the next generation"
Natural numbers are positive numbers used for counting. Integers, in addition to them, also include 0 and negative numbers. Natural numbers are denoted by ℕ, and integers by ℤ. Integers allow for subtraction without limitations, which expands the possibilities of calculation.
Natural numbers form the basic set of numbers we use for counting objects and ordering by size. They are often denoted by the symbol ℕ. There are two common definitions for this set:
The first definition is used more frequently, especially in number theory, while the second includes 0 as a natural number, which is useful in certain mathematical structures. (In many English contexts, "whole numbers" refers to {0, 1, 2, 3, ...} and "natural numbers" refers to {1, 2, 3, ...} or sometimes {0, 1, 2, 3, ...}, so clarity is important).
The set of integers, denoted by ℤ, includes all natural numbers, their opposites (negative numbers), and the number 0. Thus, the set is defined as:
ℤ = {…, -3, -2, -1, 0, 1, 2, 3, …}
Integers allow for all basic arithmetic operations, including subtraction, which is not always possible within the set ℕ (if ℕ excludes 0 and negative numbers). For example, if we subtract 5 from 3, we get -2, which is not a natural number (by the first definition) but is an integer.
Both sets have important mathematical properties:
Operations on natural numbers and integers follow specific rules:
Natural numbers and integers are fundamental mathematical sets that enable basic computational operations. While natural numbers form the basis for counting, integers expand this set with negative values, allowing for more general mathematical treatment. Their use ranges from basic arithmetic to advanced mathematical concepts.
