Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,092

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

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)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,092

Hmmm. I'm getting Nehushtan's result too, using your definition:

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,092

Ah! just seen your correction. Revised version coming up.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,092

Bob

Offline

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)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,092

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

Offline

What did you simplify in line 2? How is this relevant?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,092

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

Offline

Agnishom wrote:

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 .**143** books currently added on Goodreads

Offline

Hmm..

Thanks,

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

Pages: **1**