Does there exist a function which equals $0$ for odd inputs and $1$ for even inputs? [closed]

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Suppose $f(n)$ is a function that equals $0$ for odd inputs of $n$ and $1$ for even inputs. Note that $n$ can only be an integer. Is there a way of explicitly defining $f(n)$ so that satisfy the above conditions, without having to use a piecewise function?

analysis functions

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edited Sep 2 at 7:51

TheSimpliFire

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asked Sep 2 at 3:25

Sanjoy The Manjoy

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closed as off-topic by Nosrati, TheSimpliFire, Jyrki Lahtonen, user21820, HK Lee Sep 2 at 10:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – TheSimpliFire, Jyrki Lahtonen, user21820

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up vote
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Suppose $f(n)$ is a function that equals $0$ for odd inputs of $n$ and $1$ for even inputs. Note that $n$ can only be an integer. Is there a way of explicitly defining $f(n)$ so that satisfy the above conditions, without having to use a piecewise function?

analysis functions

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edited Sep 2 at 7:51

TheSimpliFire

10.7k62054

asked Sep 2 at 3:25

Sanjoy The Manjoy

387214

closed as off-topic by Nosrati, TheSimpliFire, Jyrki Lahtonen, user21820, HK Lee Sep 2 at 10:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – TheSimpliFire, Jyrki Lahtonen, user21820

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

Suppose $f(n)$ is a function that equals $0$ for odd inputs of $n$ and $1$ for even inputs. Note that $n$ can only be an integer. Is there a way of explicitly defining $f(n)$ so that satisfy the above conditions, without having to use a piecewise function?

analysis functions

share|cite|improve this question

edited Sep 2 at 7:51

TheSimpliFire

10.7k62054

asked Sep 2 at 3:25

Sanjoy The Manjoy

387214

Suppose $f(n)$ is a function that equals $0$ for odd inputs of $n$ and $1$ for even inputs. Note that $n$ can only be an integer. Is there a way of explicitly defining $f(n)$ so that satisfy the above conditions, without having to use a piecewise function?

analysis functions

share|cite|improve this question

edited Sep 2 at 7:51

TheSimpliFire

10.7k62054

asked Sep 2 at 3:25

Sanjoy The Manjoy

387214

share|cite|improve this question

share|cite|improve this question

edited Sep 2 at 7:51

TheSimpliFire

10.7k62054

edited Sep 2 at 7:51

TheSimpliFire

10.7k62054

edited Sep 2 at 7:51

TheSimpliFire

10.7k62054

10.7k62054

asked Sep 2 at 3:25

Sanjoy The Manjoy

387214

asked Sep 2 at 3:25

Sanjoy The Manjoy

387214

asked Sep 2 at 3:25

Sanjoy The Manjoy

387214

387214

closed as off-topic by Nosrati, TheSimpliFire, Jyrki Lahtonen, user21820, HK Lee Sep 2 at 10:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – TheSimpliFire, Jyrki Lahtonen, user21820

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Nosrati, TheSimpliFire, Jyrki Lahtonen, user21820, HK Lee Sep 2 at 10:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – TheSimpliFire, Jyrki Lahtonen, user21820

If this question can be reworded to fit the rules in the help center, please edit the question.

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add a comment | 

6 Answers
6

active

oldest

votes

up vote
11
down vote



accepted

Consider
$$
f(n):=frac1+(-1)^n2.
$$

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answered Sep 2 at 3:26

Nick Peterson

25.7k23859

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up vote
6
down vote

Another option is $$f(n) = cos^2 left(fracnpi2right)$$

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answered Sep 2 at 3:29

mweiss

17.3k23268

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up vote
6
down vote

Let $$f(n)=frac1+cos npi2$$

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answered Sep 2 at 3:30

bof

46.7k349113

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up vote
4
down vote

Yet another one: $;f(n) = 1 - leftlfloor fracn+12rightrfloor + leftlfloor fracn2rightrfloor,$.

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answered Sep 2 at 3:31

dxiv

55.8k64798

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4
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$f(n) := 1 - textmod(n, 2).$

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answered Sep 2 at 5:01

Somos

11.8k11033

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up vote
3
down vote

$$f(n) = 1 -( n -2 lfloor fracn2 rfloor)$$

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answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

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6 Answers
6

active

oldest

votes

6 Answers
6

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
11
down vote



accepted

Consider
$$
f(n):=frac1+(-1)^n2.
$$

share|cite|improve this answer

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

add a comment | 

up vote
11
down vote



accepted

Consider
$$
f(n):=frac1+(-1)^n2.
$$

share|cite|improve this answer

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

add a comment | 

up vote
11
down vote



accepted

up vote
11
down vote



accepted

Consider
$$
f(n):=frac1+(-1)^n2.
$$

share|cite|improve this answer

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

Consider
$$
f(n):=frac1+(-1)^n2.
$$

share|cite|improve this answer

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

share|cite|improve this answer

share|cite|improve this answer

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

answered Sep 2 at 3:26

Nick Peterson

25.7k23859

25.7k23859

add a comment | 

add a comment | 

up vote
6
down vote

Another option is $$f(n) = cos^2 left(fracnpi2right)$$

share|cite|improve this answer

answered Sep 2 at 3:29

mweiss

17.3k23268

add a comment | 

up vote
6
down vote

Another option is $$f(n) = cos^2 left(fracnpi2right)$$

share|cite|improve this answer

answered Sep 2 at 3:29

mweiss

17.3k23268

add a comment | 

up vote
6
down vote

up vote
6
down vote

Another option is $$f(n) = cos^2 left(fracnpi2right)$$

share|cite|improve this answer

answered Sep 2 at 3:29

mweiss

17.3k23268

Another option is $$f(n) = cos^2 left(fracnpi2right)$$

share|cite|improve this answer

answered Sep 2 at 3:29

mweiss

17.3k23268

share|cite|improve this answer

share|cite|improve this answer

answered Sep 2 at 3:29

mweiss

17.3k23268

answered Sep 2 at 3:29

mweiss

17.3k23268

answered Sep 2 at 3:29

mweiss

17.3k23268

17.3k23268

add a comment | 

add a comment | 

up vote
6
down vote

Let $$f(n)=frac1+cos npi2$$

share|cite|improve this answer

answered Sep 2 at 3:30

bof

46.7k349113

add a comment | 

up vote
6
down vote

Let $$f(n)=frac1+cos npi2$$

share|cite|improve this answer

answered Sep 2 at 3:30

bof

46.7k349113

add a comment | 

up vote
6
down vote

up vote
6
down vote

Let $$f(n)=frac1+cos npi2$$

share|cite|improve this answer

answered Sep 2 at 3:30

bof

46.7k349113

Let $$f(n)=frac1+cos npi2$$

share|cite|improve this answer

answered Sep 2 at 3:30

bof

46.7k349113

share|cite|improve this answer

share|cite|improve this answer

answered Sep 2 at 3:30

bof

46.7k349113

answered Sep 2 at 3:30

bof

46.7k349113

answered Sep 2 at 3:30

bof

46.7k349113

46.7k349113

add a comment | 

add a comment | 

up vote
4
down vote

Yet another one: $;f(n) = 1 - leftlfloor fracn+12rightrfloor + leftlfloor fracn2rightrfloor,$.

share|cite|improve this answer

answered Sep 2 at 3:31

dxiv

55.8k64798

add a comment | 

up vote
4
down vote

Yet another one: $;f(n) = 1 - leftlfloor fracn+12rightrfloor + leftlfloor fracn2rightrfloor,$.

share|cite|improve this answer

answered Sep 2 at 3:31

dxiv

55.8k64798

add a comment | 

up vote
4
down vote

up vote
4
down vote

Yet another one: $;f(n) = 1 - leftlfloor fracn+12rightrfloor + leftlfloor fracn2rightrfloor,$.

share|cite|improve this answer

answered Sep 2 at 3:31

dxiv

55.8k64798

Yet another one: $;f(n) = 1 - leftlfloor fracn+12rightrfloor + leftlfloor fracn2rightrfloor,$.

share|cite|improve this answer

answered Sep 2 at 3:31

dxiv

55.8k64798

share|cite|improve this answer

share|cite|improve this answer

answered Sep 2 at 3:31

dxiv

55.8k64798

answered Sep 2 at 3:31

dxiv

55.8k64798

answered Sep 2 at 3:31

dxiv

55.8k64798

55.8k64798

add a comment | 

add a comment | 

up vote
4
down vote

$f(n) := 1 - textmod(n, 2).$

share|cite|improve this answer

answered Sep 2 at 5:01

Somos

11.8k11033

add a comment | 

up vote
4
down vote

$f(n) := 1 - textmod(n, 2).$

share|cite|improve this answer

answered Sep 2 at 5:01

Somos

11.8k11033

add a comment | 

up vote
4
down vote

up vote
4
down vote

$f(n) := 1 - textmod(n, 2).$

share|cite|improve this answer

answered Sep 2 at 5:01

Somos

11.8k11033

$f(n) := 1 - textmod(n, 2).$

share|cite|improve this answer

answered Sep 2 at 5:01

Somos

11.8k11033

share|cite|improve this answer

share|cite|improve this answer

answered Sep 2 at 5:01

Somos

11.8k11033

answered Sep 2 at 5:01

Somos

11.8k11033

answered Sep 2 at 5:01

Somos

11.8k11033

11.8k11033

add a comment | 

add a comment | 

up vote
3
down vote

$$f(n) = 1 -( n -2 lfloor fracn2 rfloor)$$

share|cite|improve this answer

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

add a comment | 

up vote
3
down vote

$$f(n) = 1 -( n -2 lfloor fracn2 rfloor)$$

share|cite|improve this answer

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

add a comment | 

up vote
3
down vote

up vote
3
down vote

$$f(n) = 1 -( n -2 lfloor fracn2 rfloor)$$

share|cite|improve this answer

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

$$f(n) = 1 -( n -2 lfloor fracn2 rfloor)$$

share|cite|improve this answer

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

share|cite|improve this answer

share|cite|improve this answer

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

answered Sep 2 at 3:36

Ahmad Bazzi

4,5201623

4,5201623

add a comment | 

add a comment |