What is symmetric about set symmetric difference?

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Using $Delta$ for set symmetric difference,

$A Delta B$ is all the elements in exactly one of the sets but not all of them.

$A Delta B Delta C $ is all the elements in exactly one of the sets or all of them.

I appreciate there is an even number of sets in the first example and an odd number in the second (and associativity implies no order ambiguity), but what is symmetric about set symmetric difference?

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up vote
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Using $Delta$ for set symmetric difference,

$A Delta B$ is all the elements in exactly one of the sets but not all of them.

$A Delta B Delta C $ is all the elements in exactly one of the sets or all of them.

I appreciate there is an even number of sets in the first example and an odd number in the second (and associativity implies no order ambiguity), but what is symmetric about set symmetric difference?

asked 2 hours ago

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up vote
2
down vote

favorite

Using $Delta$ for set symmetric difference,

$A Delta B$ is all the elements in exactly one of the sets but not all of them.

$A Delta B Delta C $ is all the elements in exactly one of the sets or all of them.

I appreciate there is an even number of sets in the first example and an odd number in the second (and associativity implies no order ambiguity), but what is symmetric about set symmetric difference?

asked 2 hours ago

PM.

3,2082823

Using $Delta$ for set symmetric difference,

$A Delta B$ is all the elements in exactly one of the sets but not all of them.

$A Delta B Delta C $ is all the elements in exactly one of the sets or all of them.

I appreciate there is an even number of sets in the first example and an odd number in the second (and associativity implies no order ambiguity), but what is symmetric about set symmetric difference?

elementary-set-theory

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PM.

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asked 2 hours ago

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A function in two variables $f(x,y)$ is called symmetric if $f(x,y)=f(y,x)$.

It is easy to see that $AmathbintriangleB=BmathbintriangleA$, exactly because being in exactly in one of $A$ or $B$ is the same as being exactly in one of $B$ and $A$.

This is in contrast to set difference, where $Asetminus B$ is generally not the same as $Bsetminus A$.

answered 2 hours ago

Asaf Karagilaâ™¦

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1 Answer
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active

oldest

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up vote
6
down vote

accepted

A function in two variables $f(x,y)$ is called symmetric if $f(x,y)=f(y,x)$.

It is easy to see that $AmathbintriangleB=BmathbintriangleA$, exactly because being in exactly in one of $A$ or $B$ is the same as being exactly in one of $B$ and $A$.

This is in contrast to set difference, where $Asetminus B$ is generally not the same as $Bsetminus A$.

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

add a commentÂ |Â

up vote
6
down vote

accepted

A function in two variables $f(x,y)$ is called symmetric if $f(x,y)=f(y,x)$.

It is easy to see that $AmathbintriangleB=BmathbintriangleA$, exactly because being in exactly in one of $A$ or $B$ is the same as being exactly in one of $B$ and $A$.

This is in contrast to set difference, where $Asetminus B$ is generally not the same as $Bsetminus A$.

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

add a commentÂ |Â

up vote
6
down vote

accepted

A function in two variables $f(x,y)$ is called symmetric if $f(x,y)=f(y,x)$.

It is easy to see that $AmathbintriangleB=BmathbintriangleA$, exactly because being in exactly in one of $A$ or $B$ is the same as being exactly in one of $B$ and $A$.

This is in contrast to set difference, where $Asetminus B$ is generally not the same as $Bsetminus A$.

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

A function in two variables $f(x,y)$ is called symmetric if $f(x,y)=f(y,x)$.

It is easy to see that $AmathbintriangleB=BmathbintriangleA$, exactly because being in exactly in one of $A$ or $B$ is the same as being exactly in one of $B$ and $A$.

This is in contrast to set difference, where $Asetminus B$ is generally not the same as $Bsetminus A$.

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

answered 2 hours ago

Asaf Karagilaâ™¦

296k32412739

add a commentÂ |Â

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