set of Ф as { } proof of uniqueness
$begingroup$
The following set:
S = {Ф, {Ф}, {Ф, {Ф}}}
can be represented by the following string (finite sequence) of “{” and “}”:
s = { { } { { } } { { } { { } } } }
Note that the empty set Ф was written as { } and all commas were omitted.
1) Show that if a string s of “{“ and “}” represents a set S, then S is unique, i.e. two different sets are represented by two different strings.
discrete-mathematics elementary-set-theory proof-writing
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
$endgroup$
add a comment |
$begingroup$
The following set:
S = {Ф, {Ф}, {Ф, {Ф}}}
can be represented by the following string (finite sequence) of “{” and “}”:
s = { { } { { } } { { } { { } } } }
Note that the empty set Ф was written as { } and all commas were omitted.
1) Show that if a string s of “{“ and “}” represents a set S, then S is unique, i.e. two different sets are represented by two different strings.
discrete-mathematics elementary-set-theory proof-writing
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
$endgroup$
add a comment |
$begingroup$
The following set:
S = {Ф, {Ф}, {Ф, {Ф}}}
can be represented by the following string (finite sequence) of “{” and “}”:
s = { { } { { } } { { } { { } } } }
Note that the empty set Ф was written as { } and all commas were omitted.
1) Show that if a string s of “{“ and “}” represents a set S, then S is unique, i.e. two different sets are represented by two different strings.
discrete-mathematics elementary-set-theory proof-writing
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
$endgroup$
The following set:
S = {Ф, {Ф}, {Ф, {Ф}}}
can be represented by the following string (finite sequence) of “{” and “}”:
s = { { } { { } } { { } { { } } } }
Note that the empty set Ф was written as { } and all commas were omitted.
1) Show that if a string s of “{“ and “}” represents a set S, then S is unique, i.e. two different sets are represented by two different strings.
discrete-mathematics elementary-set-theory proof-writing
discrete-mathematics elementary-set-theory proof-writing
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
edited Dec 4 '18 at 17:21
Andrés E. Caicedo
65k8158246
65k8158246
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
asked Dec 4 '18 at 17:04
Mohamed MahfouzMohamed Mahfouz
1
1
add a comment |
add a comment |
1 Answer
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$begingroup$
Hint: From a (suitable) string of ${$s and $}$s, you can recover the expression a finite set written in list notation by first replacing all instances of "$}{$" by "$},{$", and then replacing all instances of "${}$" by "$varnothing$". Now use the fact that two sets are equal if and only if they contain the same elements.
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
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votes
$begingroup$
Hint: From a (suitable) string of ${$s and $}$s, you can recover the expression a finite set written in list notation by first replacing all instances of "$}{$" by "$},{$", and then replacing all instances of "${}$" by "$varnothing$". Now use the fact that two sets are equal if and only if they contain the same elements.
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
$endgroup$
add a comment |
$begingroup$
Hint: From a (suitable) string of ${$s and $}$s, you can recover the expression a finite set written in list notation by first replacing all instances of "$}{$" by "$},{$", and then replacing all instances of "${}$" by "$varnothing$". Now use the fact that two sets are equal if and only if they contain the same elements.
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
$endgroup$
add a comment |
$begingroup$
Hint: From a (suitable) string of ${$s and $}$s, you can recover the expression a finite set written in list notation by first replacing all instances of "$}{$" by "$},{$", and then replacing all instances of "${}$" by "$varnothing$". Now use the fact that two sets are equal if and only if they contain the same elements.
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
$endgroup$
Hint: From a (suitable) string of ${$s and $}$s, you can recover the expression a finite set written in list notation by first replacing all instances of "$}{$" by "$},{$", and then replacing all instances of "${}$" by "$varnothing$". Now use the fact that two sets are equal if and only if they contain the same elements.
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
answered Dec 4 '18 at 17:09
Clive NewsteadClive Newstead
50.8k474133
50.8k474133
add a comment |
add a comment |
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