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What is the sum of the rational numbers?
The sum of any finite set of rational numbers is a rational number.
If you add a rational and irrational number what is the sum?
an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
Is it true that sum of a rational number and irrational number is irrational?
Yes
Explain why the sum of a rational number and an irrational number is an irrational number?
Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)
What is the sum of any rational number and its opposite explain?
If the opposite is meant to be the additive opposite and not the multiplicative opposite, then their sum is zero. The reason is that is what defines an additive opposite!
What is the sum of the rational numbers?
The sum of any finite set of rational numbers is a rational number.
What type of number is the sum of any whole number and any rational number?
It is a rational number.
Is sum of any 2 rational number is a rational number?
True.
Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
Why is the sum of a rational number and its opposite always epual to zero?
Because that is how its additive inverse is defined!
Which number can be added to a rational number to explain that the sum of rational number and an irrational number is irrational?
Any, and every, irrational number will do.
Is the sum of a rational number and a rational number rational?
Yes.
Can you add two irrational numbers to get a rational number?
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
May the sum of a rational and an irrational number only be a rational number?
No. In fact the sum of a rational and an irrational MUST be irrational.
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
Why is the sum of a rational number and it's opposite always equal to 0?
Because the opposite of 8 for example is -8 and 8+(-8) = 0
