From: "Alberto Monteiro"
>
> Robert Shaw wrote:
> >
> >When you switch the calculator on you get a zero, but after that
> >you never touch another number key. These were scientific
> >calculators so we had ^2,^3,^-1,cos, sin, tan, cosh, sinh, tanh,
> >ln, log and their inverses plus factorial.
> >
> You don't have log in the base two, do you? I think that without
> log2 there's no way to get (x + 1) from (x).
>
> <pause to write, debug, compile and run a program>
>
> Well, I think it's not possible to get x++ using just those
> keys. I tried to generate 10000 numbers using those
> functions [except  arc-hyperbolic stuff, that are not
> functions in M$ Visual C] and I didn't even get number _3_.
>
3 is
ln(square(square(exp(square( sin(acos(ln(sqrt(exp(exp(1)))))))))))

Using hyperbolic functions, since cosh^2-sinh^2=1
you get x++= square(cosh(asinh(sqrt(x))))

If you don't use hyperbolic functions it's slightly more complicated.
You have to use 1+tan^2=sec^2 to find
x++=  1/(square(cos(atan(sqrt(x)))))
which takes one extra button press.

Of course, repeatedly incrementing is generally not the faster
way to reach an integer, but it is a proof of principle.

--
Robert


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