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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
Exercises
12. Consider the set
of all real nonzero numbers and division as a binary operation on it. Prove that
division does not have an identity element.
13. Consider the set of all real-valued functions
= f : ℝ→ℝjf is a function defined for all real numbersg:
On the set consider multiplication of functions. If f and g are two elements of , their product
is the function fg defined as (fg)(x)=f ( x)g (x) for all real numbers x. Prove that the function e (x)=1
is the identity element for t his operation. Then pr ove tha t not every function has an inverse
function
14. Consider the set A ={a, b, c} and on it consider the binary operation defined ...
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Publisher Resources

ISBN: 9780123822178