Skip to Main Content
For enterprise
For government
For higher ed
For individuals
For Content Marketing
For enterprise
For government
For higher ed
For individuals
For Content Marketing
Explore Skills
Cloud Computing
Microsoft Azure
Amazon Web Services (AWS)
Google Cloud
Cloud Migration
Cloud Deployment
Cloud Platforms
Data Engineering
Data Warehouse
SQL
Apache Spark
Microsoft SQL Server
MySQL
Kafka
Data Lake
Streaming & Messaging
NoSQL Databases
Relational Databases
Data Science
AI & ML
Generative AI
Machine Learning
Artificial Intelligence (AI)
Deep Learning
Reinforcement Learning
Natural Language Processing
TensorFlow
Scikit-Learn
Hyperparameter Tuning
MLOps
Programming Languages
Java
JavaScript
Spring
Python
Go
C#
C++
C
Swift
Rust
Functional Programming
Software Architecture
Object-Oriented
Distributed Systems
Domain-Driven Design
Architectural Patterns
IT/Ops
Security
Network Security
Application Security
Incident Response
Zero Trust Model
Disaster Recovery
Penetration Testing / Ethical Hacking
Governance
Malware
Security Architecture
Security Engineering
Security Certifications
Design
Web Design
Graphic Design
Interaction Design
Film & Video
User Experience (UX)
Design Process
Design Tools
Business
Agile
Project Management
Product Management
Marketing
Human Resources
Finance
Team Management
Business Strategy
Digital Transformation
Organizational Leadership
Soft Skills
Professional Communication
Emotional Intelligence
Presentation Skills
Innovation
Critical Thinking
Public Speaking
Collaboration
Personal Productivity
Confidence / Motivation
Features
All features
AI Academy
Courses
Certifications
Interactive learning
Live events
Answers
Insights reporting
Radar Blog
Buy Courses
Plans
Sign In
Try Now
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
Then,
which
one
of
the
two
principles
should
be
used
in
a
proof
by
induction?
The
first
answer
is
that
since
the
two
principles
are
logically
equivalent,
it
really
does
not
make
any
difference.
One
could
always
use
the
Stro ng
Principle
of
Mathemati cal
Inductio n
si nce
its
inductive
hypothe sis
seems
to
co ver
more
ground.
In
general,
when
proving
equalities,
the
Principle
of
Mathematical
Induction
is
sufficient.
For
some
mathematicians
it
is
a
matter
of
elegance
and
beauty
to
use
as
little
mathematical
machinery
as
pos-
sible
when
constructing
a
proof,
and
therefore
t hey
prefer
to
use
the
Principle
of
Mathematical
Induction
whenever
possible. ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial
You might also like
Discrete Structures, Logic, and Computability, 4th Edition
James L. Hein
Computational Mathematics, 2nd Edition
Robert E. White
Discrete Mathematical Structures
U.S. Gupta
Differential Equations, 2nd Edition
Steven G. Krantz
Publisher Resources
ISBN: 9780123822178