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To restate; we can say: 1) Assume that an x exists such that 2=x^x^x^x^... 2) Then x = sqrt(2) 3) sqrt(2)^10 = 32 Therefore there is no such x. In very bri
by vessenes 16y ago
To restate; we can say:
1) Assume that an x exists such that 2=x^x^x^x^...
2) Then x = sqrt(2)
3) sqrt(2)^10 = 32
Therefore there is no such x.
In very brief, we can say that there is no number so infinitesimally close to 1 that infinite exponentiation of it does not 'blow up'.
Or to pull a Calc 1 term: x^x^x^x^... does not converge for all x >1. Simple.
- RiderOfGiraffes 16y agoI don't understand why your step 3 is relevant. Observe that using r=sqrt(2) we have that the sequence r, r^r, r^r^r, r^r^r^r, ... does converge to 2. We are not performing arbitrarily large exponentiation of x. Or, to pull a Calc 1 term, x^x^x^... does converge for x=sqrt(2).
- Lozzer 16y agoIt's the difference between x^(x^(x... and ((x^x)^x)...