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gnox at May 10, 2018 11:33 AM

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Then there will be
[ω exponents of the exponents]
Cantor gives no other way of writing these. But

Suppose that instead of ω² we write ω(1,2).
For ω³ ω4, we write ω(1,3), ω(1,4).
For ωω, etc. we write ω(1,1,2), ω(1,1,3).
So that (ωω…)5·6 will be written ω(6·5·4).
Then we shall at length get ω(1,1,ω) which
may write ω(1,1,1,2). So we shall get
w(1,1,1,1,2) w(1,1,1,1,1,2),
w(1,1,1,1,1,1,2) and after all these

50

50

Then there will be
[ω exponents of the exponents]
Cantor gives no other way of writing these. But

Suppose that instead of ω² we write ω(1,2).
For ω³ ω4, we write ω(1,3), ω(1,4).
For ωω, etc. we write ω(1,1,2), ω(1,1,3).
So that (ωω…)5·6 will be written ω(6.5.4).
Then we shall at length get ω(1,1,ω) which
may write ω(1,1,1,2). So we shall get
w(1,1,1,1,2) w(1,1,1,1,1,2),
w(1,1,1,1,1,1,2) and after all these