Math Is Fun Forum

Karimazer1

Guest

Inequality Proof Help!

Want to prove three different things; this should all work for my whole answer to be corrrect but in the last stages I am struggling with the proof/confirmation.

Ok, 0<pi<1, i=1,2,3,4 .  BUT the SUM =1, so Sum p1+p2+p3+p4 =1. But none of them can be 0 or 1, all inbetween whilst summing to one.

Now, given this.... I want to understand WHY these inequalities CANNOT hold:

1.  9(p1) > 6(p1) + 6(p4)
2.  9(p2) + 9(p3) > 6(p1) + 6(p4)
3.  9(p4) > 6(p1) + 6(p4)

Treat all of these seperately! I don't know if this is correct or not, basically I think all is correct until this point, but this is the checking part...i.e. if these DO NOT hold, I am correct. Thank you I really cannot wait until I see the response!!!!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Inequality Proof Help!

Those do not always hold. It would be good if you posted the inequality you are strugling with.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Karimazer1

Guest

Re: Inequality Proof Help!

All three must hold given the assumptions. I want to contradict why these can not work. So for the first one for example, even though p2 and p3 are not there, they are both still positive values less than one and greater than 0. Does this help?

Thank you!!

Karimazer1

Guest

Re: Inequality Proof Help!

THANKS. I found a mistake because of your comment, thank you, i now have new inequalities after looking back, i will attempt. hopefully will not need anyhelp, i hope! let me see now i will work on it!!

Karimazer1

Guest

Re: Inequality Proof Help!

Ahhhhhh. I am so bad at this.

Ok, completely new assumptions. Discard the above. I didn't include r.

So, 0<p<1 so that (1-p) + p = 1. (Probability)
Also, 0<q<1 so that (1-q) + q = 1.

Now;

1. p+q > 1+ (pq)/2 - (I have cancelled this down to this, why can this NOT work? I can't understand the intuition / maths)
2. p+q > 6/15 + 2pq - (I have cancelled this down to this, why can this NOT work? I can't understand the intuition / maths)
3. 1 > p + q + pq - (I have cancelled this down to this, why can this NOT work? I can't understand the intuition / maths)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality Proof Help!

Hi;

p+q > 1+ (pq)/2 -

What comes after the minus sign in all three problems?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Karimazer1

Guest

Re: Inequality Proof Help!

I am so sorry bobby and everyone, nothing comes after the negative sign!! nothing at all, i just put that to add the note for the brackets!

Karimazer1

Guest

Re: Inequality Proof Help!

Thank you Bobby!

But why does p+q = 1 ?

If p = 0.2 (so 1-p=0.8) and q=0.3 (so 1-q = 0.7) then p+q = 0.5 whilst still being viable given restrictions on p and q... ?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality Proof Help!

Hi;

When you use the variables p and q and mention the word probability it is standard for the relationship between p and q to be p+q=1. That is what confused me. Is this the case?

Also p+q>1 +(pq)/2 is sometimes true and sometimes false.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Karimazer1

Guest

Re: Inequality Proof Help!

Apologies, I see what you mean, normally that is the case but here it is not because it is an extention of that form in this example.

It is not the case, here p + (1-p) = 1, and q + (1-q) = 1.

(1-q) and (1-p) don't feature here in that form because I had to use them to derive the given inequalities. So I guess here, p+(1-p)+q+(1-q)=2 ? But that cancel's out to 2=2 so i guess is not useful...

I look forward to your reply!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality Proof Help!

Hi;

Is sometimes true and sometimes false.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Karimazer1

Guest

Re: Inequality Proof Help!

Thank you!

Do the other ones work too? This is bad news for me, means I messed up somewhere. I just tried to input e.g. 0.9 =p and 0.9 = q and it did not work, you are correct. darn!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality Proof Help!

Hi;

Is sometimes true and sometimes false.

Is sometimes true and sometimes false.

Please post the original problem and maybe something can be done.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.