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Irrational Numbers are infinitely dense so that there are infinitely many irrational numbers between any to numbers. In fact, there are more irrational numbers between any two numbers than there are rational numbers in total!

Q: What is the closest irrational number to 13?

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Any irrational number, when added to 13, will produce an irrational number.

Any irrational number will do.

13 is rational

The set of irrational numbers is infinitely dense. As a result there are infinitely many irrational numbers between any two numbers. So, if any irrational number, x, laid claim to be the closest irrational number to 3, it is possible to find infinitely many irrational numbers between x and 3. Consequently, the claim cannot be valid.

18 and 20

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Any irrational number, when added to 13, will produce an irrational number.

Any irrational number, when added to 13, will produce an irrational number.

There is no such number. Between any two irrational numbers there are infinitely many irrational numbers. So, the claim that x is the irrational number closest to ten can be demolished by the fact that there are infinitely many irrational numbers between x and 10 (or 10 and x).

6.000........

There is no such number. Irrational numbers are infinitely dense. Given any number near 13, there are more irrational numbers between that number and 13 than there are rational numbers in all.

Any irrational number will do.

Yes, it is an irrational number.

It is a rational number

-13 is a rational number

13 is rational

The set of irrational numbers is infinitely dense. As a result there are infinitely many irrational numbers between any two numbers. So, if any irrational number, x, laid claim to be the closest irrational number to 3, it is possible to find infinitely many irrational numbers between x and 3. Consequently, the claim cannot be valid.

First - 50 is a rational number, not an irrational number since it can be represented as a ratio of integers, i.e. 50/1 With that said: the two integers closest to it are 49 and 51