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Searching for an asymptotic to exp[0.5]
More on that :



Long ago , I was challenged on sci.math to answer my own question.

There cannot be a bijection from exp^[1/2](w) to w nor 2^w.

Here is why :

Let f(x) be exp^[1/2](x) + o(1).

If card f(w) = card w then

card f(f((w)) = card f( card f(w) ) = card f(w) = card(w)

But f(f(w)) = 2^w

Contradiction

If card f(w) = card 2^w then

card f(f(w)) = card f ( card f(w) ) = card f ( 2^w ) = card(2^(2^w))

But f(f(w)) = 2^w

Contradiction

Likewise for exp^[a](w).


Regards

Tommy1729
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Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/04/2016, 08:16 PM

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