answersLogoWhite

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

User Avatar

Wiki User

14y ago

What else can I help you with?

Related Questions

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 is the sum of two irrational numbers?

It may be a rational or an irrational number.


The sum of rational numbers and an irrational number?

It is always an irrational number.


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.


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.


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.


Can 2 irrational add to an irrational number?

Yes. The sum of two irrational numbers can be rational, or irrational.


The sum of two irrational is always irrational?

No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.