Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.
Natural numbers are actually closed under addition. If you add any two if them, the result will always be another natural number.
No. It is not a group.
No.
Yes, when you add any group of natural numbers, the sum will also be a natural number.
All real numbers are commutative under addition and multiplication.
Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.
There are four properties of a real number under addition and multiplication. These properties are used to aid in solving algebraic problems. They are Commutative, Associative, Distributive and Identity.
Natural numbers are actually closed under addition. If you add any two if them, the result will always be another natural number.
No. It is not a group.
No.
Yes, when you add any group of natural numbers, the sum will also be a natural number.
The two are counts and so natural numbers. The set of natural numbers is closed under addition.
They form a commutative ring in which the primary operation is addition and the secondary operation is multiplication. However, it is not a field because it is not closed under division by a non-zero element.
The commutative property holds for all numbers under addition, regardless of whether they are positive or negative - the sign of the number stays with the number, for example: -2 + 5 = (-2) + 5 = 5 + (-2) = 5 + -2 -2 + -5 = (-2) + (-5) = (-5) + (-2) = -5 + -2 Subtraction is not commutative, but when subtraction is taken as adding the negative of the second number, the commutative property of addition holds, for example: 5 - 2 ≠ 2 - 5 but: 5 - 2 = 5 + -2 = 5 + (-2) = (-2) + 5 = -2 + 5
Yes, because naturals are counting numbers, {1,2,3...} and any natural number added by another natural number has to be a natural. Think of a number line, and your adding the natural numbers. The sum has to be natural, so yes it is closed.
The Abelian (commutative) property of integers under addition.