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Does every rational number have an additive inverse and why?
yes
What is every positive number and its negative pair called?
That would be the set of all non-zero numbers. If by number you actually meant whole numbers, that is integers, then it would be the set of all non-zero integers. They are also called Additive Inverses. For example, -5 is the additive inverse of 5, because 5 + (-5) = 0. Similarly, 7 is the additive inverse of -7 because (-7) + 7 = 0.
Every positive rational number and its negative pair?
Every positive rational number and its negative are the two square roots of the same positive rational number.
What number produces rational numbers when multiplied by 5?
Every rational number does.
Is every real number is rational?
No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.
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
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.
Why does every rational number have an additive inverse?
It is a fundamental requirement of algebraic structures called groups.
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).
