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Numbers and Proofs
About this book
'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow.Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.
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Information
10
NUMBERS
AND
PROOFS
Figure
1.1
All
proofs
must
start
somewhere
Figure
1.1
is
actually
very
useful
for
making
two
points
quite
forcefully.
First
we
ask:
do
the
assertions
denoted
by
A,
B,
C,
H
and
MI
have
some
kind
of
universal
quality?
Don't
they
depend
on
anything
at
all?
Can
they
not
be
deduced
from
anything
more
'basis'?
In
fact,
in
Figure
1.1,
B
represents
the
assertion
that
l
p
=
1,
so
one
could
argue
that
B
is
a
consequence
of
the
equality
1-1
=
1
(and
MI).
Then
you
may
ask:
what
is
1·
1
=
1
a
consequence
of?
What,
indeed,
is
meant
by
T?
(As
we
are
now
getting
a
bit
too
philosophical
we
take
this
no
further.)
It
is
clear
that
we
cannot
keep
regressing
in
this
way
for
ever.
Accordingly,
in
the
proofs
that
we
look
at
later,
we
shall
be
happy
to
accept
certain
easily
believed,
simple
assertions
as
being
unquestionably
true
(for
example,
that
l
20
=
1)
and
not
Table of contents
- Front Cover
- Numbers and Proofs
- Copyright Page
- Table of Contents
- Preface
- Chapter 1. The Need for Proof
- Chapter 2. Statements and Connectives
- Chapter 3. True or False?
- Chapter 4. Sets, Negations, Notations and Functions
- Chapter 5. Proofs...for All
- Chapter 6. There Exist...Proofs
- Chapter 7. Principle of Mathematical Induction
- Chapter 8. The Integers and the Rational Numbers
- Chapter 9. The Rational Numbers and the Real Numbers
- Chapter 10. The Real Numbers and the Complex Numbers
- Chapter 11. Guessing, Analogy and Transformation
- Chapter 12. Generalization and Specialization
- Chapter 13. Fallacies and Paradoxes — and Mistakes
- Chapter 14. A Mixed Bag
- Chapter 15. Hints/Answers to the Exercises
- References
- Index
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Yes, you can access Numbers and Proofs by Reg Allenby in PDF and/or ePUB format, as well as other popular books in Mathematics & Logic in Mathematics. We have over one million books available in our catalogue for you to explore.