# Finding Power Set of Power Set of an Empty Set?

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## 13 Replies - 32635 Views - Last Post: 10 April 2011 - 12:07 PM

### #1 mrsenim

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# Finding Power Set of Power Set of an Empty Set?

Posted 22 February 2010 - 11:19 AM

Hello!

I am not sure if this is the right place for this post but I couldn't find any other suitable place for this question so please forgive me if there's something wrong.

I am trying to solve P(P(P(Ø))) but I am not sure if my answer is correct

Please tell me which of the following is correct (if any).

1-
```P(P(P(Ø))) = {Ø, {Ø}, {{Ø}}, {Ø, {Ø}}}
```

2-
```P(P(P(Ø))) = {Ø, {{Ø}}, {{Ø}}, {Ø, {Ø}}}
```

Thanks!

This post has been edited by mrsenim: 22 February 2010 - 11:30 AM

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## Replies To: Finding Power Set of Power Set of an Empty Set?

### #2 r.stiltskin

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 22 February 2010 - 01:20 PM

Why don't you try building it up systematically and write them out one after another, e.g.:
{}
P({}) =
P(P({})) =
P(P(P({}))) =

ps: How did you produce the "oslash" symbol?

### #3 mrsenim

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 06:13 AM

r.stiltskin, on 22 February 2010 - 12:20 PM, said:

Why don't you try building it up systematically and write them out one after another, e.g.:
{}
P({}) =
P(P({})) =
P(P(P({}))) =

I tried, but I am not sure if answer is correct or not. Here is the solution.

```P(Ø) = ?

Ø has no elements therefore P(Ø) will contain 2^0=1 element, that is
P(Ø) = {Ø}

What will be the power set of the above set?

P(P(Ø)) = ?

P(Ø) has one element therefore P(P(Ø)) will contain 2^1=2 elements, that is
P(P(Ø)) = {Ø, {Ø}}

What will be the power set of the above set?

P(P(P(Ø))) = ?

P(P(Ø)) has two elements therefore P(P(P(Ø))) will contain 2^2=4 elements, that is
P(P(P(Ø))) = {Ø, {Ø}, {{Ø}}, {Ø, {Ø}}}

```

r.stiltskin, on 22 February 2010 - 12:20 PM, said:

ps: How did you produce the "oslash" symbol?

This is Ø(phi). A Greek Letter to show empty set. It can be copied from "Accessories" -> "system tools" -> "Character Map" -> "Lucida Console"

Anyways Thank You.

This post has been edited by mrsenim: 23 February 2010 - 06:15 AM

### #4 r.stiltskin

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 06:59 AM

mrsenim, on 23 February 2010 - 08:13 AM, said:

... It can be copied from "Accessories" -> "system tools" -> "Character Map" -> "Lucida Console"

That only applies to Windows. Is there a code that you are copying? How is it shown in your Post/Edit box for this forum?

### #5 r.stiltskin

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 08:17 AM

Testing Ø.

Hah. I can cut and paste it from your post. Don't know why I didn't think of that before.

### #6 mrsenim

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 09:50 AM

r.stiltskin, on 23 February 2010 - 05:59 AM, said:

Thank You!

r.stiltskin, on 23 February 2010 - 05:59 AM, said:

That only applies to Windows.

True

r.stiltskin, on 23 February 2010 - 05:59 AM, said:

Is there a code that you are copying? How is it shown in your Post/Edit box for this forum?

No it is not a code. I have taken it from character map. Well I am not a computer master what actually is, I need various symbols while I am working in mathematics, logic and set theory. For example Λ (And), ν (Or). There are lots of symbols in character map but all of them do not work in all programs. Mostly I work on notepad and "Lucida Console" work in notepad.

Regarding How is it shown in my Post/Edit box, necessity is the mother of invention, I though if they work in notepad then they must work in textarea. I tried and it worked. Otherwise what I would had done is I simply would had edited my post and used "Empty" instead of Ø.

This post has been edited by mrsenim: 23 February 2010 - 10:03 AM

### #7 r.stiltskin

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 10:15 AM

mrsenim, on 23 February 2010 - 11:50 AM, said:

I need various symbols while I am working in mathematics, logic and set theory.

If you are serious about this you should learn to use LaTeX to write your papers. For Windows platforms, have a look at TeXnicCenter.

### #8 mrsenim

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 11:09 AM

Ok, I will give it a try. Thank You.

### #9 modi123_1

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 11:50 AM

r.stiltskin, on 22 February 2010 - 02:20 PM, said:

Why don't you try building it up systematically and write them out one after another, e.g.:
{}
P({}) =
P(P({})) =
P(P(P({}))) =

ps: How did you produce the "oslash" symbol?

Side note - you can use the windows alt key codes..

Press and hold ALT then type 237 gets you: φ
ALT + 232 = Φ (upper case phi)

http://customcompute.../alt_codes1.htm

### #10 mrsenim

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 12:01 PM

modi123_1, on 23 February 2010 - 10:50 AM, said:

r.stiltskin, on 22 February 2010 - 02:20 PM, said:

Why don't you try building it up systematically and write them out one after another, e.g.:
{}
P({}) =
P(P({})) =
P(P(P({}))) =

ps: How did you produce the "oslash" symbol?

Side note - you can use the windows alt key codes..

Press and hold ALT then type 237 gets you: φ
ALT + 232 = Φ (upper case phi)

http://customcompute.../alt_codes1.htm

Yes it is also mentioned in "character Map". There is shortcut key for many symbols but it only works with number keypad while your Num lock is on.

It doesn't work with other number keys which are on left side under function keys.

### #11 r.stiltskin

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 12:50 PM

Nope. Alt+[a number] is a keyboard shortcut that switches my Firefox to another browser tab.

### #12 modi123_1

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 01:23 PM

r.stiltskin, on 23 February 2010 - 01:50 PM, said:

Nope. Alt+[a number] is a keyboard shortcut that switches my Firefox to another browser tab.

You are in a text box, right? I've used firefox for some time and that doesn't seem to be a functionality that I can replicate.

### #13 r.stiltskin

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 23 February 2010 - 05:05 PM

Yeah. You're using Windows, right? According to this mozilla code table Ctrl + [number] should swap tabs in your browser. In Linux, it's Alt + [number].

This post has been edited by r.stiltskin: 23 February 2010 - 05:05 PM

### #14 mentallysound

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## Re: Finding Power Set of Power Set of an Empty Set?

Posted 10 April 2011 - 12:07 PM

thank you very much mrsenim
i was too entrapped in this very problem