Question

Please solve the problem

Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers.

Rational numbers can be written in the form p/q, where p and q are integers. So 42 and -11/3 are rational, while and √2 are not. It’s a very basic property, so you’d think we can easily tell when a number is rational or not, right?

Meet the Euler-Mascheroni constant , which is a lowercase Greek gamma. It’s a real number, approximately 0.5772, with a closed form that’s not terribly ugly; it looks like the image above.

The sleek way of putting words to those symbols is “gamma is the limit of the difference of the harmonic series and the natural log.” So it’s a combination of two very well-understood mathematical objects. It has other neat closed forms, and appears in hundreds of formulas.

But somehow, we don’t even know if is rational. We’ve calculated it to half a trillion digits, yet nobody can prove if it’s rational or not. The popular prediction is that is irrational. Along with our previous example +e, we have another question of a simple property for a well-known number, and we can’t even answer it.

Answer 1

Answer:

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