I'm thinking of a number between 1 and 5. Trophy to winner.

I'm thinking of a number between 1 and 5.  One guess per person.  First person to guess the number correctly will get a trophy from me simply saying "your name won the I'm thinking of a number between 1 and 5 contest!" and I'll even let you choose whichever standard set chess.com trophy you want me to give you.  (Isn't that tempting!)

Now, before we begin, I'm going to give you a hint that shows I'm willing to make it easier, because I like you.  As you may have noticed, I said a number between 1 and 5, but I didn't say it was inclusive.  So, that means the number can't actually be 1 or 5. 

You may wonder how you will know if I change the number or pick the winner  based on favoritism?   I assure you that will not happen. I have integrity.  However as an act of good faith, I am also willing to use any online escrow service of your choice if you are willing to pay for that service.  Because I have nothing to hide, except the number.

But alas it is that very same aforementioned integrity that compels me to inform you at this very moment that the number I'll pick won't be an integer and it will have potentially a very large number of digits following the decimal point. So, of course there are an infinite number of possibilities.  So you may just want to run out and pick up a lottery ticket and share the winnings with me for inspiring you to do so.

Good luck!

666!

No, no, no... not the tatoo on my forehead, ... a number between 1 and 5!

What, do you want some kind of trophy because I violated the terms of the agreement, in that I haven't actually thought of a number yet?  I would have to strive for something people wouldn't get, so it wouldn't be pi, but since I don't have a number, I can't prove it wouldn't be pi.

Just let me know how you want to proceed.

Of course, paK0666 was not eligible for such a concession because her guess was out of bounds as per the stated constraints of the problem.

would you please be so kind and not adress me as a female?

thank you very much =)

also you started your post with "I'm thinking..." which implies you already thought of the number

Oh, sorry the icon, small, at a distance has an effeminate quality, or so I presumed. But that doesn't mean anything other, than an unconscious force of habit.  Well, it was true, I was thinking of a number of numbers, but I hadn't pinned it down to a specific number.  A number of numbers is a number, after all.. I didn't say a number of what.

Anyway, my error to not have a number in mind, so do you want a trophy?  And if so, which one?  You win because of my breech of contract.

1.618. The number PHI it is called.

Naw man. I gave you a trophy.  Delete it only if you wish to.

e = 2 . 7 1 8 2 8 ...

No thanks, I can live without a trophy, just give me another guess once you have a specific number ;)

Lot's of people say they can live without a trophy.  But what kind of life is that, really?  I mean, come on.  Anyway, I've already given the trophy away.   Now I'm thinking of an indescribable feeling.  Or am I feeling an indescribable thought?  I'll get back to you about that.

What kind of number is it? Natural, rational, real or complex? Or even something else?

There is no clean way to order complex numbers, so "any number between 1 and 5" pretty much rules out the nonreal complex numbers. It leaves all real numbers, which includes integers and rationals.

I was able to determine the property that defines your number, but I didn't bother calculating it. Here you go : noting x your number, x is between 1 and 5 and verifies

ln(1 + x + x^2/2 + x^3/(2*3) + x^4/(4*3*2) + ... + x^n/(n*(n-1)*...2) + ...) = x

(where ln() is the natural logarithm ie in base e)

Determining him at any precision is then trivial with a computer.

I guess I'm too late. I got held up in traffic.