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Jul
14
accepted order of infinite countable ordinal numbers
Jul
14
comment order of infinite countable ordinal numbers
Thanks for the proof; much to learn.
Jul
14
revised order of infinite countable ordinal numbers
added 3 characters in body
Jul
13
revised order of infinite countable ordinal numbers
edited title
Jul
13
comment order of infinite countable ordinal numbers
@AsafKaragila I tried rewriting to make my question clearer.
Jul
13
revised order of infinite countable ordinal numbers
added 69 characters in body
Jul
13
revised order of infinite countable ordinal numbers
added 60 characters in body; edited title
Jul
13
comment order of infinite countable ordinal numbers
@AsafKaragila They are definitely NOT all equal. My question was clearly talking about ordinal arithmetic and the relative sizes or ordinal numbers
Jul
13
comment order of infinite countable ordinal numbers
@AsafKaragila I wanted to know the order of the sizes
Jul
13
comment order of infinite countable ordinal numbers
I don't think this should be marked as duplicate; I would like someone to verify that size ordering is apparently: $${^\omega} 2 \qquad 2^\omega = \omega,\qquad \omega^2,\qquad, \omega^\omega, \qquad, {^\omega} \omega$$
Jul
13
comment order of infinite countable ordinal numbers
ok, presumably that is consistent, but it seems a bit odd, that such a fast growing sequence is regarded as smaller than $\omega^2$
Jul
13
comment order of infinite countable ordinal numbers
The defining sequence for $^{\omega} 2$ is $2\;\;2^2\;\;2^{2^2}\;\;2^{2^{2^2}}\;\;2^{2^{2^{2^2}}}....$
Jul
13
asked order of infinite countable ordinal numbers
Jun
21
revised Limit involving tetration
added 6 characters in body
Jun
18
revised Limit involving tetration
fixed small typo
Jun
15
revised Limit involving tetration
added Edgar's website as another reference
Jun
15
revised Limit involving tetration
approximation for ln(ln(eta+1/m))
Jun
15
comment Limit involving tetration
Also, notice that $\pi\sqrt{\frac{2\eta\cdot n}{e}} \approx \sqrt{10.49n}$, so this is close to the Op's original $\sqrt{10n}$ term.
Jun
15
revised Limit involving tetration
clarification
Jun
15
revised Limit involving tetration
clarification