Math Is Fun Forum

Yep.

How many cases do you have when they get one each?

Hi bobbyn

I'm getting twice your answer for the second one.

You're welcome.

Well, basically, yes. You need infinite "cuts" to "reach" 0.24999...

For a nice proof of that fact, look at Joel's answer.

That is a know fact. The usual discussion is whether 1=0.999... The answer is yes and there are much simpler proofs than the one given in that image. The proof in that image is, also, not a very rigorous proof, but it does provide a nice way to visualise both of the decimal expansions.

I entered the same thing you did and got 455 of them, as it should be. I'm not sure what's with that.

For the issue of order, try entering the numbers in the correct order, ie., enter 9,9n,9b,9#,9+,3,...

So, your comment in post #4 is not a good one, then?

Those are not the forum rules, but rather your own. What prevents EVW from developing her own set of rules for blurting answers out?

Oh, sorry. It's not exactly perfect, but it is wglhat it is.

I see you know about the Catalan numbers.

Also, congrats for learning LaTeX. Tip: you can use \binom{}{} for the binomial coefficient.

You've done such things yourself, bobbym.

Ok, so, if I got this correctly, the Euler angles just set an objects orientation in its own inertial system using rotations around all three axes. Is that correct.

If yes, that means that the velocity vector has to have a default starting orientation. What did you choose for that orientation?