0
There is no answer.
If the sum is taken for irrationals positive irrationals only, then the answer is clearly + infinity, since the irrationals increase without limit.
But there are negative irrationals so we need to consider the sum of irrationals from - infinity to + infinity. Each irrational has a matching negative irrational and these two sets are exhaustive. So, each can be paired off, and one might think that the sum of an infinite pairs of zeros is zero, right?
NO, unfortunately not. The logic fails when the sum is over infinitely many terms as is illustrated below:
1-1+1-1 ... = 1+(-1+1)+(-1+1) ... = 1+0+0 ... = 1
or
1-1+1-1 ... = (1-1)+(1-1)+ ... = 0+0+ ... = 0
Incidentally, the above example was used to "prove" that 1 = 0
What else can I help you with?
Sum of two irrational numbers?
Can be rational or irrational.
What is the classification of the sum rational and irrational numbers?
Irrational
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
If you add two irrational numbers do you get an irrational number?
Not necessarily. The sum of two irrational numbers can be rational or irrational.
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
What will be the sum of a rational number and an irrational number?
It will be irrational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
The sum of rational numbers and an irrational number?
It is always an irrational number.
What is the sum of two irrational numbers?
It may be a rational or an irrational number.
Is the sum of two irrational numbers also an irrational number?
Not necessarily. 3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.
What is the sum or difference of the any two irrational numbers?
The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.
Can 2 irrational add to an irrational number?
Yes. The sum of two irrational numbers can be rational, or irrational.
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.
