It is very inspiring to understand “infinity” (the state of being infinite – which means it is not finite) through FGH and infinite ordinals. Just on their own, infinite ordinals are quite “useless”. They need to be realized through diagonalization and so a finite natural number must be there.
I used the word “realization” – and it possibly implies that for things to be “real”, it should be definite and finite.
The function f in FGH seems to be the interlink between heaven and earth. While the infinite ordinals are flying in the sky, higher and higher, they are summoned from time to time to build great things on earth.
(And then some uncountable infinite ordinals are pulling up the countable infinite ordinals from beyond the Universe.)
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