Multiple Choice The number 1 has this property, since the only positive integer not exceeding 1 is 1 itself, and therefore the sum is 1. This is a nonconstructive proof, because an example for which the statement is true is given. The number 1 has this property, since the only positive integer not exceeding 1 is 1 itself, and therefore the sum is 1. This is a constructive proof, because an example for which the statement is true is given. If the sum of the positive integers less than a positive integer is not equal to the positive integer, then the sum will exceed the positive integer. This is a constructive proof, because the statement proved by contradiction.
Multiple Choice The number 1 has this property, since the only positive integer not exceeding 1 is 1 itself, and therefore the sum is 1. This is a nonconstructive proof, because an example for which the statement is true is given. The number 1 has this property, since the only positive integer not exceeding 1 is 1 itself, and therefore the sum is 1. This is a constructive proof, because an example for which the statement is true is given. If the sum of the positive integers less than a positive integer is not equal to the positive integer, then the sum will exceed the positive integer. This is a constructive proof, because the statement proved by contradiction.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please make answer easy to read
Transcribed Image Text:Identify the correct proof and the type of proof of the statement that there is a positive integer that equals the sum of the positive integers not exceeding it.
Multiple Choice
The number 1 has this property, since the only positive integer not exceeding 1 is 1 itself, and therefore the sum is 1. This is a nonconstructive proof, because an example for which the
statement is true is given.
The number 1 has this property, since the only positive integer not exceeding 1 is 1 itself, and therefore the sum is 1. This is a constructive proof, because an example for which the
statement is true is given.
If the sum of the positive integers less than a positive integer is not equal to the positive integer, then the sum will exceed the positive integer. This is a constructive proof, because
the statement is proved by contradiction.
If the sum of the positive integers less than a positive integer is not equal to the positive integer, then the sum will exceed the positive integer. This is a nonconstructive proof,
because the statement is proved by contradiction.
Expert Solution
Step 1
Given that there is a positive integer that equals the sum of the positive integers not exceeding it.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
