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 16 mins ago
user549397
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asked 55 mins ago
J.SJ.S
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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 16 mins ago
user549397
1,2181315
asked 55 mins 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 16 mins ago
user549397
1,2181315
asked 55 mins 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 16 mins ago
user549397
1,2181315
asked 55 mins 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.
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edited 16 mins ago
user549397
1,2181315
asked 55 mins 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 16 mins ago
user549397
1,2181315
edited 16 mins ago
user549397
1,2181315
edited 16 mins ago
user549397
1,2181315
1,2181315
asked 55 mins 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 55 mins ago
J.SJ.S
62
asked 55 mins 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.
Check out our Code of Conduct.
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 |
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 38 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 38 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 38 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 38 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 38 mins ago
David KDavid K
53.4k341115
answered 38 mins ago
David KDavid K
53.4k341115
answered 38 mins ago
David KDavid K
53.4k341115
answered 38 mins ago
David KDavid K
53.4k341115
53.4k341115
add a comment |
add a comment |
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