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O'Reilly Platform
book
The Nuts and Bolts of Proofs, 4th Edition
by
Antonella Cupillari
January 2011
Beginner content level
Beginner
296 pages
11h 43m
English
Academic Press
Content preview from
The Nuts and Bolts of Proofs, 4th Edition
In
general,
the
value
of
ε
that
will
enable
us
to
complete
the
proof
depends
on
the
behavior
of
the
function
around
c
,
and
smaller
values
of
ε
aremorelikelytowork.In
Example
4.5.15
we
used
ε
=1/2,
but,
if
one
looks
carefully
thr ough
the
ste ps
of
the
p roof,
any
value
of
ε
smaller
than
or
equal
t o
1
(which
is
one
of
the
values
of
the
function)
wo uld
be
a cceptab le.
Thus,
in
gener al
the
choice
of
ε
is
not
unique.
The
proof
te chni qu es
i llustr ate d
in
the
exam ple s
ar e
not
always
easy
to
im ple ment .
As
one
adva nces
in
the
study
of
real
analysis,
one
builds
more
and
more
tools
to
deal
efficiently
with
the
nonexistence
of
limits.
Some
of
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Publisher Resources
ISBN: 9780123822178