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#1 2014-05-01 20:49:53
Set Theory Identity
Prove that:
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#3 2014-05-01 21:24:51
Re: Set Theory Identity
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2014-05-01 21:56:05
- Bob
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Re: Set Theory Identity
Looks to me like you have 'proved' it with the diagrams. All you need to do is convert that into set statements and it is done.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#5 2014-05-01 22:05:17
Re: Set Theory Identity
What are set statements?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#7 2014-05-01 22:43:43
Re: Set Theory Identity
Sorry, it is supposed to be This:
Prove that:
I can figure it out myself if you can explain how to get the third line fromt the second
Last edited by Agnishom (2014-05-01 22:47:05)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2014-05-01 22:51:15
- Bob
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- Registered: 2010-06-20
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Re: Set Theory Identity
Hmmm. I'm getting Nehushtan's result too, using your definition:
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#9 2014-05-01 22:52:02
- Bob
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- Registered: 2010-06-20
- Posts: 10,643
Re: Set Theory Identity
Ah! just seen your correction. Revised version coming up.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#11 2014-05-01 22:56:03
- Bob
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- Registered: 2010-06-20
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Re: Set Theory Identity
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#12 2014-05-01 22:57:12
Re: Set Theory Identity
Nehushtan,
I see it all. The problem seems to be with the proof.
Please Tell me how I can show
bob,
Sorry, I do not get it.
Last edited by Agnishom (2014-05-01 22:58:14)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#13 2014-05-01 23:04:00
- Bob
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- Registered: 2010-06-20
- Posts: 10,643
Re: Set Theory Identity
Oh.
line 1: I used your definition for the triangly thing.
line 2: I simplified it. Couldn't make a dash work as in A-dash = not A so I used a wobbly over tilde thingy.
phi is the empty set.
As for this:
Use the distributivity laws
In A AND in the union = just A
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#14 2014-05-01 23:12:42
Re: Set Theory Identity
What did you simplify in line 2? How is this relevant?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#15 2014-05-02 00:23:45
- Bob
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- Registered: 2010-06-20
- Posts: 10,643
Re: Set Theory Identity
I'll try it in more detail:
So A big triangled with the intersection is (A less the intersection) united with (the intersection less A)
A less the intersection is the bits of A without the bits in B.
The intersection without A is nothing at all so the empty set.
Unite these.
But everything in a set plus the empty set is still just that set so
This is just the definition of \, hence
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#16 2014-05-02 00:28:45
- Nehushtan
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- Registered: 2013-03-09
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Re: Set Theory Identity
Please Tell me how I can show
Note that is a subset of . In general, if then .
Proof:
We must prove that both
and . is clear since is a subset of .To prove the other inclusion, suppose
and let . . If we are done. If then, since , we have as well. In either case . Hence .240 books currently added on Goodreads
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#17 2014-05-02 02:11:09
Re: Set Theory Identity
Hmm..
Thanks,
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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