Is ∅ ∈ { {∅} } true?
$begingroup$
If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?
Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?
elementary-set-theory
edited 32 mins ago
user549397
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$endgroup$
add a comment |
$begingroup$
If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?
Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?
elementary-set-theory
edited 32 mins ago
user549397
1,2181315
asked 1 hour ago
J.SJ.S
62
New contributor
J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?
Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?
elementary-set-theory
edited 32 mins ago
user549397
1,2181315
asked 1 hour ago
J.SJ.S
62
New contributor
J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
If $ {emptyset} ∈ {emptyset,{emptyset}} $ is true, does it mean this $ emptyset in {{emptyset}} $ true ? If it is not, why it is false?
Also, does $ {{emptyset}}$ mean ${emptyset,{emptyset,{emptyset}}}$ ?
elementary-set-theory
elementary-set-theory
edited 32 mins ago
user549397
1,2181315
asked 1 hour ago
J.SJ.S
62
New contributor
J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 32 mins ago
user549397
1,2181315
asked 1 hour ago
J.SJ.S
62
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J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 32 mins ago
user549397
1,2181315
edited 32 mins ago
user549397
1,2181315
edited 32 mins ago
user549397
1,2181315
1,2181315
asked 1 hour ago
J.SJ.S
62
New contributor
J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
J.SJ.S
62
asked 1 hour ago
J.SJ.S
62
62
New contributor
J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
J.S is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
1 Answer
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$begingroup$
The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$
The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.
The first element is $emptyset.$ The second element is ${emptyset}.$
Is one of those two elements exactly equal to ${emptyset}$?
The notation ${ {emptyset}}$ describes a set with one element.
That element is ${emptyset}.$
Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
Hint: there's only one element you have to check.
The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
One element is $emptyset$ and the other is
${emptyset, {emptyset}}.$
So this is definitely not the same thing as any set that has only one element.
answered 54 mins ago
David KDavid K
53.4k341115
$endgroup$
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1 Answer
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$begingroup$
The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$
The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.
The first element is $emptyset.$ The second element is ${emptyset}.$
Is one of those two elements exactly equal to ${emptyset}$?
The notation ${ {emptyset}}$ describes a set with one element.
That element is ${emptyset}.$
Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
Hint: there's only one element you have to check.
The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
One element is $emptyset$ and the other is
${emptyset, {emptyset}}.$
So this is definitely not the same thing as any set that has only one element.
answered 54 mins ago
David KDavid K
53.4k341115
$endgroup$
add a comment |
$begingroup$
The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$
The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.
The first element is $emptyset.$ The second element is ${emptyset}.$
Is one of those two elements exactly equal to ${emptyset}$?
The notation ${ {emptyset}}$ describes a set with one element.
That element is ${emptyset}.$
Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
Hint: there's only one element you have to check.
The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
One element is $emptyset$ and the other is
${emptyset, {emptyset}}.$
So this is definitely not the same thing as any set that has only one element.
answered 54 mins ago
David KDavid K
53.4k341115
$endgroup$
add a comment |
$begingroup$
The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$
The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.
The first element is $emptyset.$ The second element is ${emptyset}.$
Is one of those two elements exactly equal to ${emptyset}$?
The notation ${ {emptyset}}$ describes a set with one element.
That element is ${emptyset}.$
Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
Hint: there's only one element you have to check.
The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
One element is $emptyset$ and the other is
${emptyset, {emptyset}}.$
So this is definitely not the same thing as any set that has only one element.
answered 54 mins ago
David KDavid K
53.4k341115
$endgroup$
The notation $a in A$ says that among the elements of $A$ there is one element that is exactly equal to $a.$
The notation ${emptyset, {emptyset}}$ describes a set with exactly two elements.
The first element is $emptyset.$ The second element is ${emptyset}.$
Is one of those two elements exactly equal to ${emptyset}$?
The notation ${ {emptyset}}$ describes a set with one element.
That element is ${emptyset}.$
Which element of ${ {emptyset}}$ do you think is exactly equal to $emptyset$?
Hint: there's only one element you have to check.
The notation ${emptyset, {emptyset, {emptyset}}}$ again describes a set with two elements.
One element is $emptyset$ and the other is
${emptyset, {emptyset}}.$
So this is definitely not the same thing as any set that has only one element.
answered 54 mins ago
David KDavid K
53.4k341115
answered 54 mins ago
David KDavid K
53.4k341115
answered 54 mins ago
David KDavid K
53.4k341115
answered 54 mins ago
David KDavid K
53.4k341115
53.4k341115
add a comment |
add a comment |
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