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Ladder

Ordinals — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. basevaluein hereditary baseordinal242^2ω^ω3263^2·2 + 3·2 + 2ω^2·2 + ω·2 + 24414^2·2 + 4·2 + 1ω^2·2 + ω·2 + 15605^2·2 + 5·2ω^2·2 + ω·26836^2·2 + 6 + 5ω^2·2 + ω + 571097^2·2 + 7 + 4ω^2·2 + ω + 481398^2·2 + 8 + 3ω^2·2 + ω + 391739^2·2 + 9 + 2ω^2·2 + ω + 21021110^2·2 + 10 + 1ω^2·2 + ω + 11125311^2·2 + 11ω^2·2 + ω1229912^2·2 + 11ω^2·2 + 11G(4) written in hereditary base b, the base bumped to b+1, then one subtractedthe integers keep rising, and the ordinals fall at every single step — which is why it has to stop

    A sequence that explodes and still stops

    Goodstein's sequence starting at 4 climbs past any number you care to name and reaches zero after about ten to the hundred and twenty million steps. The proof that it stops is a second sequence, running alongside it, that goes down.

    rung 1 · logic

All ladders