Is this cool with you?

bobbym · 2011-08-25 20:38:16

Hi gAr;

Thanks for looking at it.

bobbym · 2011-08-31 02:17:32

New Problem:

You are given an integer t ( 0 to 9 ). You can use decimal points, multiplication, addition, division, subtraction, parentheses and exponentiation only. How close can you get to Euler's number using t only? You can use t as many times as you want.

A says) I got it using 3 t"s.
B says) Nonsense! Not with 3 you didn't.
C says) 4 t's is about right.
D says) Yep!
E says) 3 is definitely not the best.

What is t and what is your expression?

bobbym · 2011-09-03 22:43:00

New Problem!

E does a bit of numeric work for someone. She is asked to Hornerize the LHS. She gets the RHS.

A says) It is going to be hard to check if she is right. You have to expand that to
be sure.

B says) You only have to try two numbers for x.

C says) Holy Zeilberger! B is right!

D says) I do not think so...

A says) Kaboobly doo, no amount of numbers plugged in can verify that expression.
You should go back to school B! Finite tests are not infinity! You can not prove things by plugging in three or four numbers and then saying it is true. Mathematics B, is a deductive science.

E says) Stop hollering A. B is on the right track but it will take a couple of numbers.

B says) Nope, two is plenty.

Who is right?

gAr · 2011-09-03 23:57:36

Hi bobbym,

bobbym · 2011-09-04 00:11:13

Hi gAr;

gAr · 2011-09-04 00:19:44

Hi bobbym,

bobbym · 2011-09-04 00:35:37

Hi gAr;

gAr · 2011-09-04 00:50:28

Hi bobbym,

Meanwhile,

bobbym · 2011-09-04 01:02:59

Hi gAr;

gAr · 2011-09-04 01:30:40

Hi bobbym,

Thanks.
And I don't have another answer for #1030.

bobbym · 2011-09-04 01:38:58

The general case:

For 2 polynomials:

Choose

Then trying the points from S is all that is required to determine equality.

If the coefficients of P(x) and Q(x) are positive. Then only 2 values are necessary.

1) If P(1) = Q(1)

and

2) P(P(1)+1) = Q(Q(1)+1)

Then P(x) = Q(x)

gAr · 2011-09-04 04:10:54

Hi bobbym,

P(P(1)+1) = Q(Q(1)=1)

Is that Q(1)+1 instead of Q(1)=1 ?

bobbym · 2011-09-04 10:43:13

Hi gAr;

Yikes an ugly typo! You are correct, I have cleaned up the mess in the above post. Thanks.

gAr · 2011-09-04 15:17:33

Hi bobbym,

Okay.
I don't understand what's unique about P(1)+1
Will this work for polynomials only with positive coefficients?

bobbym · 2011-09-04 15:57:22

Hi gAr;

I do not get the reason either. That one is for positive
coefficients only. The other is for any two polynomials.

Zeilberger mentions it. It is part of their method of proving theorems by trying a finite amount of cases. Exactly what they tell not to do in mathematics. But yet Ramanujan did it and the experimental mathematicians are following.

gAr · 2011-09-04 16:40:41

Hi,

Hmmm, okay.

bobbym · 2011-09-04 17:08:43

Hi gAr;

Is that a hmmm, meaning, ah maybe. Or is it meaning, that bobbym is sure weird. Personally, I am going with the weird one.

The general one I know is true the second one I never heard of.

gAr · 2011-09-04 17:35:54

"Hmmm" as in I'm not totally sure with any answer yet!

bobbym · 2011-09-04 19:04:45

Hi gAr;

I know, I am just kidding.

gAr · 2011-09-04 22:10:47

Hi bobbym,

I knew you were kidding!

bobbym · 2011-09-04 23:25:08

Hi;

How could you know?

gAr · 2011-09-04 23:46:46

Hi,

Because you aren't weird!

bobbym · 2011-09-04 23:47:40

Hi gAr;

I am going to change my image. Have you noticed weird people
are smarter?

gAr · 2011-09-05 00:02:22

Hi bobbym,

Okay.
Yes, I have. What's "important" to the majority doesn't matter to them.

bobbym · 2011-09-05 00:04:10

Hi gAr;

To be brilliant one has to be a little crazy. Or maybe very crazy. A little bit uncaring.

Math Is Fun Forum

#1026 2011-08-25 20:38:16

Re: Is this cool with you?

#1027 2011-08-31 02:17:32

Re: Is this cool with you?

#1028 2011-09-03 22:43:00

Re: Is this cool with you?

#1029 2011-09-03 23:57:36

Re: Is this cool with you?

#1030 2011-09-04 00:11:13

Re: Is this cool with you?

#1031 2011-09-04 00:19:44

Re: Is this cool with you?

#1032 2011-09-04 00:35:37

Re: Is this cool with you?

#1033 2011-09-04 00:50:28

Re: Is this cool with you?

#1034 2011-09-04 01:02:59

Re: Is this cool with you?

#1035 2011-09-04 01:30:40

Re: Is this cool with you?

#1036 2011-09-04 01:38:58

Re: Is this cool with you?

#1037 2011-09-04 04:10:54

Re: Is this cool with you?

#1038 2011-09-04 10:43:13

Re: Is this cool with you?

#1039 2011-09-04 15:17:33

Re: Is this cool with you?

#1040 2011-09-04 15:57:22

Re: Is this cool with you?

#1041 2011-09-04 16:40:41

Re: Is this cool with you?

#1042 2011-09-04 17:08:43

Re: Is this cool with you?

#1043 2011-09-04 17:35:54

Re: Is this cool with you?

#1044 2011-09-04 19:04:45

Re: Is this cool with you?

#1045 2011-09-04 22:10:47

Re: Is this cool with you?

#1046 2011-09-04 23:25:08

Re: Is this cool with you?

#1047 2011-09-04 23:46:46

Re: Is this cool with you?

#1048 2011-09-04 23:47:40

Re: Is this cool with you?

#1049 2011-09-05 00:02:22

Re: Is this cool with you?

#1050 2011-09-05 00:04:10

Re: Is this cool with you?

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