Mixing
Binary function which added to itself, arguments switched, gives a constant
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up vote
2
down vote
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Say I have the function
$$
f_1(x, y) = fracxx + y labelatag1
$$
or
$$
f_2(x, y) = fracy - xx + y labelbtag2
$$
or
$$
f_3(x, y) = x - y labelctag3
$$
Then $f(a, b) + f(b, a) = c$ for any $a$ and $b$.
Is there a name for such a property?
If there is no short name for it, how would you describe it?
So far I've said that the function and its commutation(?) are additively inverse, around some value $d = c/2$. In the case of $(refb)$ and $(refc)$ that value would be $0$, in $(refa)$ it would be $0.5$
functions terminology
asked Jul 19 at 19:22
AkselA
1136
add a comment |Â
up vote
2
down vote
favorite
Say I have the function
$$
f_1(x, y) = fracxx + y labelatag1
$$
or
$$
f_2(x, y) = fracy - xx + y labelbtag2
$$
or
$$
f_3(x, y) = x - y labelctag3
$$
Then $f(a, b) + f(b, a) = c$ for any $a$ and $b$.
Is there a name for such a property?
If there is no short name for it, how would you describe it?
So far I've said that the function and its commutation(?) are additively inverse, around some value $d = c/2$. In the case of $(refb)$ and $(refc)$ that value would be $0$, in $(refa)$ it would be $0.5$
functions terminology
asked Jul 19 at 19:22
AkselA
1136
I have no idea of the name but describing it as "$f(a,b) + f(b,a)=c$ for all $a,b,$" seems a more than adequate description to me. Or $f(a,b) = -f(b,a) + C$.
– fleablood
Jul 19 at 19:29
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Say I have the function
$$
f_1(x, y) = fracxx + y labelatag1
$$
or
$$
f_2(x, y) = fracy - xx + y labelbtag2
$$
or
$$
f_3(x, y) = x - y labelctag3
$$
Then $f(a, b) + f(b, a) = c$ for any $a$ and $b$.
Is there a name for such a property?
If there is no short name for it, how would you describe it?
So far I've said that the function and its commutation(?) are additively inverse, around some value $d = c/2$. In the case of $(refb)$ and $(refc)$ that value would be $0$, in $(refa)$ it would be $0.5$
functions terminology
asked Jul 19 at 19:22
AkselA
1136
Say I have the function
$$
f_1(x, y) = fracxx + y labelatag1
$$
or
$$
f_2(x, y) = fracy - xx + y labelbtag2
$$
or
$$
f_3(x, y) = x - y labelctag3
$$
Then $f(a, b) + f(b, a) = c$ for any $a$ and $b$.
Is there a name for such a property?
If there is no short name for it, how would you describe it?
So far I've said that the function and its commutation(?) are additively inverse, around some value $d = c/2$. In the case of $(refb)$ and $(refc)$ that value would be $0$, in $(refa)$ it would be $0.5$
functions terminology
asked Jul 19 at 19:22
AkselA
1136
edited Jul 19 at 20:09
asked Jul 19 at 19:22
AkselA
1136
asked Jul 19 at 19:22
AkselA
1136
asked Jul 19 at 19:22
AkselA
1136
1136
I have no idea of the name but describing it as "$f(a,b) + f(b,a)=c$ for all $a,b,$" seems a more than adequate description to me. Or $f(a,b) = -f(b,a) + C$.
– fleablood
Jul 19 at 19:29
add a comment |Â
I have no idea of the name but describing it as "$f(a,b) + f(b,a)=c$ for all $a,b,$" seems a more than adequate description to me. Or $f(a,b) = -f(b,a) + C$.
– fleablood
Jul 19 at 19:29
I have no idea of the name but describing it as "$f(a,b) + f(b,a)=c$ for all $a,b,$" seems a more than adequate description to me. Or $f(a,b) = -f(b,a) + C$.
– fleablood
Jul 19 at 19:29
I have no idea of the name but describing it as "$f(a,b) + f(b,a)=c$ for all $a,b,$" seems a more than adequate description to me. Or $f(a,b) = -f(b,a) + C$.
– fleablood
Jul 19 at 19:29
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
In the special case when $c=0$ it's called an alternating function. I don't think it has a name for general $c$.
We do have in general that $f(x,y)-frac c2$ is alternating, though.
answered Jul 19 at 19:26
Arthur
98.8k793174
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
In the special case when $c=0$ it's called an alternating function. I don't think it has a name for general $c$.
We do have in general that $f(x,y)-frac c2$ is alternating, though.
answered Jul 19 at 19:26
Arthur
98.8k793174
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
add a comment |Â
up vote
3
down vote
accepted
In the special case when $c=0$ it's called an alternating function. I don't think it has a name for general $c$.
We do have in general that $f(x,y)-frac c2$ is alternating, though.
answered Jul 19 at 19:26
Arthur
98.8k793174
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
In the special case when $c=0$ it's called an alternating function. I don't think it has a name for general $c$.
We do have in general that $f(x,y)-frac c2$ is alternating, though.
answered Jul 19 at 19:26
Arthur
98.8k793174
In the special case when $c=0$ it's called an alternating function. I don't think it has a name for general $c$.
We do have in general that $f(x,y)-frac c2$ is alternating, though.
answered Jul 19 at 19:26
Arthur
98.8k793174
answered Jul 19 at 19:26
Arthur
98.8k793174
answered Jul 19 at 19:26
Arthur
98.8k793174
answered Jul 19 at 19:26
Arthur
98.8k793174
98.8k793174
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
add a comment |Â
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
For any non-zero $c$ value, $f (x,y)-c/2$ would be an alternating function :)
– CiaPan
Jul 19 at 19:32
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
@CiaPan That's right. It even says so in my answer :)
– Arthur
Jul 19 at 19:35
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
Didn't see that part when I was writing my comment.
– CiaPan
Jul 19 at 19:39
add a comment |Â
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I have no idea of the name but describing it as "$f(a,b) + f(b,a)=c$ for all $a,b,$" seems a more than adequate description to me. Or $f(a,b) = -f(b,a) + C$.
– fleablood
Jul 19 at 19:29