The additive inverse of EVERY positive rational number is a negative number.
For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
Yes.
It is a fundamental requirement of algebraic structures called groups.
The additive inverse of EVERY positive rational number is a negative number.
yes
For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.
The additive inverse states that a number added to its opposite will equal zero. A + (-A) = 0. The "opposite" number here is the "negative" of the number. For any number n, the additive inverse is (-1)n. So therefore yes.
Yes.
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
Yes.
It is a fundamental requirement of algebraic structures called groups.
One example would be a Galois Field size 4 (ie GF(4)). Here, the elements are {0,1,2,3} and every element is its own additive inverse.
To form the additive inverse, negate all parts of the complex number → 8 + 3i → -8 - 3i The sum of a number and its additive inverse is 0: (8 + 3i) + (-8 - 3i) = (8 + -8) + (3 + -3)i = (8 - 8) + (3 - 3)i = 0 + 0i = 0.
It is a tautological description of one of the basic properties of numbers used in the branch of mathematics called Analysis: Property 2: there exists an additive identity, called 0; for every number n: n + 0 = 0 + n = n. Property 3: there exists an additive inverse, of every number n denoted by (-n) such that n + (-n) = (-n) + n = 0 (the additive identity).
The additive inverse of a number is the value that, when added to the original number, results in a sum of zero. In this case, the additive inverse of 22 would be -22, as 22 + (-22) equals zero. The additive inverse is essentially the negative version of the original number.