Give an example of a function from $mathbb N to mathbb N$ that satisfied
For each of the following properties give an example of a function from $mathbb N to mathbb N$ that satisfied:
(a) one-to-one but not onto
(b) onto but not one-to-one
(c) both onto and one-to-one
(d) neither one-to-one nor onto
In part (b), the model answer uses $f(n)= max{}$, I got confused, what's the relationship between maximum and surjective function?
functions discrete-mathematics
edited Dec 10 '18 at 2:21
Dando18
4,66741235
asked Dec 10 '18 at 2:17
CCola
275
add a comment |
For each of the following properties give an example of a function from $mathbb N to mathbb N$ that satisfied:
(a) one-to-one but not onto
(b) onto but not one-to-one
(c) both onto and one-to-one
(d) neither one-to-one nor onto
In part (b), the model answer uses $f(n)= max{}$, I got confused, what's the relationship between maximum and surjective function?
functions discrete-mathematics
edited Dec 10 '18 at 2:21
Dando18
4,66741235
asked Dec 10 '18 at 2:17
CCola
275
The model answer makes no sense. The maximum of what?
– fleablood
Dec 10 '18 at 2:33
add a comment |
For each of the following properties give an example of a function from $mathbb N to mathbb N$ that satisfied:
(a) one-to-one but not onto
(b) onto but not one-to-one
(c) both onto and one-to-one
(d) neither one-to-one nor onto
In part (b), the model answer uses $f(n)= max{}$, I got confused, what's the relationship between maximum and surjective function?
functions discrete-mathematics
edited Dec 10 '18 at 2:21
Dando18
4,66741235
asked Dec 10 '18 at 2:17
CCola
275
For each of the following properties give an example of a function from $mathbb N to mathbb N$ that satisfied:
(a) one-to-one but not onto
(b) onto but not one-to-one
(c) both onto and one-to-one
(d) neither one-to-one nor onto
In part (b), the model answer uses $f(n)= max{}$, I got confused, what's the relationship between maximum and surjective function?
functions discrete-mathematics
functions discrete-mathematics
edited Dec 10 '18 at 2:21
Dando18
4,66741235
asked Dec 10 '18 at 2:17
CCola
275
edited Dec 10 '18 at 2:21
Dando18
4,66741235
asked Dec 10 '18 at 2:17
CCola
275
edited Dec 10 '18 at 2:21
Dando18
4,66741235
edited Dec 10 '18 at 2:21
Dando18
4,66741235
edited Dec 10 '18 at 2:21
Dando18
4,66741235
4,66741235
asked Dec 10 '18 at 2:17
CCola
275
asked Dec 10 '18 at 2:17
CCola
275
asked Dec 10 '18 at 2:17
CCola
275
275
The model answer makes no sense. The maximum of what?
– fleablood
Dec 10 '18 at 2:33
add a comment |
The model answer makes no sense. The maximum of what?
– fleablood
Dec 10 '18 at 2:33
The model answer makes no sense. The maximum of what?
– fleablood
Dec 10 '18 at 2:33
The model answer makes no sense. The maximum of what?
– fleablood
Dec 10 '18 at 2:33
add a comment |
1 Answer
1
active
oldest
votes
Some possibilities:
$1)$ How about $f(x)=2x,,forall xinmathbb N$.
$2)$ $f(x)=begin{cases}1, x=1\x-1, xneq1end{cases}$
$3)f(x)=x,,forall xinmathbb N$
$4)f(x)=1,,forall xinmathbb N$
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Some possibilities:
$1)$ How about $f(x)=2x,,forall xinmathbb N$.
$2)$ $f(x)=begin{cases}1, x=1\x-1, xneq1end{cases}$
$3)f(x)=x,,forall xinmathbb N$
$4)f(x)=1,,forall xinmathbb N$
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
add a comment |
Some possibilities:
$1)$ How about $f(x)=2x,,forall xinmathbb N$.
$2)$ $f(x)=begin{cases}1, x=1\x-1, xneq1end{cases}$
$3)f(x)=x,,forall xinmathbb N$
$4)f(x)=1,,forall xinmathbb N$
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
add a comment |
Some possibilities:
$1)$ How about $f(x)=2x,,forall xinmathbb N$.
$2)$ $f(x)=begin{cases}1, x=1\x-1, xneq1end{cases}$
$3)f(x)=x,,forall xinmathbb N$
$4)f(x)=1,,forall xinmathbb N$
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
Some possibilities:
$1)$ How about $f(x)=2x,,forall xinmathbb N$.
$2)$ $f(x)=begin{cases}1, x=1\x-1, xneq1end{cases}$
$3)f(x)=x,,forall xinmathbb N$
$4)f(x)=1,,forall xinmathbb N$
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
answered Dec 10 '18 at 2:50
Chris Custer
10.8k3824
10.8k3824
add a comment |
add a comment |
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The model answer makes no sense. The maximum of what?
– fleablood
Dec 10 '18 at 2:33