He then shows that if there were a proof of a contradiction, the reduction procedure would result in an infinite descending sequence of ordinals smaller than ? 0 produced by a primitive recursive operation on proofs corresponding to a quantifier-free formula.
22.
On the other hand, if the final note was to be a breve " ( sine perfectione ) ", this was signaled by a change in the noteheads themselves : the descending sequence of square heads was replaced with a single diagonal beam ( alt = two square black noteheads in ascending order connected by a vertical stroke ).
23.
The essential notes of the violin theme are B-C-D-E-F-E, and the essential notes of the piano theme are : G-C-E-G-F-G ( the rest of the piano theme is a descending sequence of ascending seconds : G-A-F-G-E-F-D-E ).
24.
The " molad " interval as an exact improper fraction = 29 + 12 / 24 + 44 / 1440 + ( 10 / 3 ) / 86400 = 765433 / 25920 days, where the denominator 25920 is the number of parts per day ( each part equals 1 / 18 minute or 10 / 3 seconds ) and one can alternatively write the numerator in the interesting descending sequence 765432 + 1.
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