May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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34 DISCRETE MATHEMATIC..._
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3. QED Conjunction
Of
course, we could also expand the step for s ending in 1 into a careful series
of
inequalities.
Now consider
sO.
We
hope that what we did to make the
s1
case work does not mess up the
sO
case. But
we have to check.
The first statement is easy.
It
follows from the first statement
of
the inductive hypothesis for s, because
we
are not increasing the number
of
01s.
But now the second statement involves more work. The difficulty is that the new string ends in 0,
which means that we have to show the stronger inequality in the second statement. But to do this we might
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