Question

The set ( mathbb{Z} ) of integers is countable. Define a function ( f: mathbb{N} ightarrow mathbb{Z} ) [ f(n)=left{egin{array}{ll} frac{n-1}{2}, & n=1,3,5, ldots ldots \ frac{-n}{2}, & n=2,4,6 ldots ldots . end{array} ight. ] Find another function ( h: mathbb{N} ightarrow mathbb{Z} ).

          The set ( mathbb{Z} ) of integers is countable. Define a function ( f: mathbb{N} 
ightarrow mathbb{Z} )
[
f(n)=left{egin{array}{ll}
frac{n-1}{2}, & n=1,3,5, ldots ldots \
frac{-n}{2}, & n=2,4,6 ldots ldots .
end{array}
ight.
]

Find another function ( h: mathbb{N} 
ightarrow mathbb{Z} ).

$The set ( mathbbZ ) of integers is countable. Define a function ( f: mathbbN ightarrow mathbbZ ) [ f(n)=lefteginarrayll fracn-12, n=1,3,5, ldots ldots frac-n2, n=2,4,6 ldots ldots . endarray ight. ] Find another function ( h: mathbbN ightarrow mathbbZ ).$

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A Complete Resource Book in Mathematics for JEE Main

Dinesh Khattar 2019 Edition

Chapter 2

Instant Answer

Solved by Expert Vincenzo Zaccaro

04/28/2024

Step 1

It maps natural numbers to integers in a specific way: if the natural number is odd, it maps it to a positive integer or zero (since $\frac{n-1}{2}$ for $n=1$ is zero), and if the natural number is even, it maps it to a negative integer. Now, we need to find Show more…

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