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Is a additive inverse of any rational number a negative number?
The additive inverse of EVERY positive rational number is a negative number.
Why does every rational number have a additive inverse?
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.
What is the aditive inverse property?
For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.
Does every natural number have an additive inverse?
Yes. Just put a minus sign in front of it. Note that except for the zero, the additive inverse is no longer a natural number.
Does every integer have an additive inverse?
Yes.
Is a additive inverse of any rational number a negative number?
The additive inverse of EVERY positive rational number is a negative number.
Does every rational number have an additive inverse and why?
yes
Does every rational number have an additive inverse?
Yes.
Why does every rational number have a additive inverse?
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.
What is the aditive inverse property?
For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.
How does every rational number have an additive inverse?
By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0Then p/q + (-p/q) = [p + (-p)] /q = 0/q.Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
Does every integer has an additive inverse?
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.
Does every natural number have an additive inverse?
Yes. Just put a minus sign in front of it. Note that except for the zero, the additive inverse is no longer a natural number.
Does every integer have an additive inverse?
Yes.
When the additive inverse of a number equal to the absolute value of the number?
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.
What is the additive inverse of the complex number 8 plus 3i?
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.
What is a number added to its additive inverse will always have a sum of zero?
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).
