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How do you prove that the sum of a rational number and its additive inverse is zero?
Wiki User
∙ 13y ago
I can give you an example and prove it:
eg. take the rational no. 2......hence its additive inverse ie. its opposite no. will be -2
now lets add:
=(2)+(-2)
=2-2
=0
it means that the opposite no.s. get cancelled and give the answer 0
this is the same case for sum of a rational no. and its opposite no. to be ZERO
Wiki User
∙ 13y ago
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Who was the first person to prove that pi was not a rational number?
Johann Heinrich Lambert
Is 11 squared rational or irrational?
It's the ratio of 121 to 1, so it's rational. I think the square of any rational number is a rational number. In fact, I'm sure of it, because I know how I could prove it.
Are all rational numbers whole numbers prove your answer?
No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.
How can you prove that 6.34 is a rational number?
(A): 6.34*100 = 634 so 6.34 = 634/100 a ratio of two integers and so a rational number. (B): 6.34 is a terminating decimal - with two non-zero digits after the decimal point. So again, it is a rational number.
Math help can anyone show you how to do this please Prove or disprove that if a and b are rational number then a to the power of b is rational?
2 and 1/2 are rational numbers, but 2^(1/2) is the square root of 2. It is well known that the square root of 2 is not rational.
How do I prove the additive inverse is unique?
assume its not. make two cases show that the two cases are equal
What models can you to prove that opposites combine to zero?
There is not much to prove there; opposite numbers, by which I take you mean "additive inverse", are defined so that their sum equals zero.
Which number can be multiplied to a rational number to explain that the product of two rational numbers is rational?
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
Who was the first person to prove that pi was not a rational number?
Johann Heinrich Lambert
Why does zero have no multiplicative inverse?
The multiplicative inverse is defined as: For every number a ≠ 0 there is a number, denoted by a⁻¹ such that a . a⁻¹ = a⁻¹ . a = 1 First we need to prove that any number times zero is zero: Theorem: For any number a the value of a . 0 = 0 Proof: Consider any number a, then: a . 0 + a . 0 = a . (0 + 0) {distributive law) = a . 0 {existence of additive identity} (a . 0 + a . 0) + (-a . 0) = (a . 0) + (-a . 0) = 0 {existence of additive inverse} a . 0 + (a . 0 + (-a . 0)) = 0 {Associative law for addition} a . 0 + 0 = 0 {existence of additive inverse} a . 0 = 0 {existence of additive identity} QED Thus any number times 0 is 0. Proof of no multiplicative inverse of 0: Suppose that a multiplicative inverse of 0, denoted by 0⁻¹, exists. Then 0 . 0⁻¹ = 0⁻¹ . 0 = 1 But we have just proved that any number times 0 is 0; thus: 0⁻¹ . 0 = 0 Contradiction as 0 ≠ 1 Therefore our original assumption that there exists a multiplicative inverse of 0 must be false. Thus there is no multiplicative inverse of 0. ---------------------------------------------------- That's the mathematical proof. Logically, the multiplicative inverse undoes multiplication - it is the value to multiply a result by to get back to the original number. eg 2 × 3 = 6, so the multiplicative inverse is to multiply by 1/3 so that 6 × 1/3 = 2. Now consider 2 × 0 = 0, and 3 × 0 = 0 There is more than one number which when multiplied by 0 gives the result of 0. How can the multiplicative inverse of multiplying by 0 get back to the original number when 0 is multiplied by it? In the example, it needs to be able to give both 2 and 3, and not only that, distinguish which 0 was formed from which, even though 0 is a single "number".
Is 11 squared rational or irrational?
It's the ratio of 121 to 1, so it's rational. I think the square of any rational number is a rational number. In fact, I'm sure of it, because I know how I could prove it.
Are all rational numbers whole numbers prove your answer?
No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.
Who was t he first person to prove that pi is not a rational number?
Johann Heinrich Lambert
Who was the 1st person to prove that pi is not a rational number?
Johann Lambert
What fractional form of 9.546 to prove that it is a rational number?
9.546 as an improper fraction in its simplest form is 4773/500 which proves that it is a rational number
How can you determine if a number is rational?
If the number can be expressed as a ratio of two integer (the second not zero) then the number is rational. However, it is not always a simple matter to prove that if you cannot find such a representation, then the number is not rational: it is possible that you have not looked hard enough!
