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## #1 Re: Help Me ! » What must be added? » 2012-09-19 01:22:18

Let
.

Expanding,

.

Comparing coefficients gives

.

:

## #2 Re: Jokes » Random jokes I come across » 2012-07-22 04:06:59

A scientist was carrying out an experiment on electricity. Suddenly his apparatus blew up. When he realized what had gone wrong, he was horrified at what he had accidentally done. He couldn't believe he had just touched the anode of his electrolytic cell.

He was positively shocked.

## #3 Re: Dark Discussions at Cafe Infinity » Words that contain AEIOU, in any order, each vowel exactly once » 2012-07-14 20:32:43

JaneFairfax wrote:

AEOIU
archegonium
pandemonium
praseodymium

appressorium

## #4 Re: Dark Discussions at Cafe Infinity » Words that contain AEIOU, in any order, each vowel exactly once » 2012-06-01 22:40:49

JaneFairfax wrote:

IAEOU
dichlamydeous
filamentous
intravenous
ligamentous
micaceous

## #5 Re: Help Me ! » Minimum of the function » 2012-03-27 21:57:14

The melee of terms in the summation is just to confuse you. Don't be sidetracked by it. Just focus on this question: If
(where
are real numbers) what can you say about
themselves?

Try
.

## #7 Re: Exercises » Bafflers? » 2012-03-23 03:25:53

bobbym wrote:

Baffler #4

Batches of 15 steel balls are given to you. 14 of them are exactly alike. One ball is slightly heavier in each batch. You have a two pan balance that you can use to weigh the balls against each other. As the plant manager you are given the job of designing a method to find the heavier ball in each batch. Each weighing of any group of balls is considered one move. What is the average number of moves to determine the heavier ball for each batch?

## #8 Re: Help Me ! » Even and Odd functions » 2012-03-23 02:16:22

bob bundy wrote:

So an even function = an odd function    =><=

It isn't exactly a contradiction. There is exactly one function that is both odd and even and that's
.

## #9 Re: Euler Avenue » Proof for definitions of e? » 2012-03-01 08:10:36

Alex23 wrote:

What is the proof for the two common definitions of e? The continuous compounding and the sum over inverse factorials?

Hi Alex23.

Definitions are not supposed be proved. It makes no sense to "prove" a definition. I think what you're looking for is a proof of the equivalence of two definitions of e.

## #10 Jokes » John & Jo » 2012-03-01 06:52:00

Sylvia104
Replies: 4

Jo: Hi!
John: Hi!
John: John McEnroe. What's yours?
Jo: Jo King.
John: You cannot be serious!

## #11 Jokes » Syllogism » 2012-02-19 14:34:46

Sylvia104
Replies: 18

I am nobody.
Nobody is perfect.
Therefore I am perfect.

## #12 Re: Help Me ! » a²+4ab+b² » 2012-02-19 13:37:23

Write
as
by putting
and
. Conversely any number of the form
can be written as
by putting
and
. Hence

and
, take
and
. Then

## #13 Re: Help Me ! » A bird flies into a train » 2011-10-12 04:02:11

I still don't understand why the bird has to accelerate. Can't it just fly in such a way that its forward speed is the same as the train's so it can just enter the train by slipping in sideways? Its overall velocity will of course be greater than 50mph, but the forward component of its velocity is 50mph. The train passengers will see it move sideways, but it will be stationary to them in the forwardsbackwards direction.

## #14 Re: Help Me ! » A bird flies into a train » 2011-10-12 03:41:50

bobbym wrote:

But even before you land, your motion will have a small additional velocity over the trains. Otherwise you would not have entered the train. Relative to the train once in the car you are travelling forward. That is why you roll forward.

What if you don't land? What if you can fly like the bird and you enter the train without making contact with any part of it?

bobbym wrote:

I have placed the link you want in post #3.

Thanks!

bobbym wrote:

By the way, I wished you have told me his name is Melonhead.

Me too.

## #15 Re: Help Me ! » A bird flies into a train » 2011-10-12 03:00:07

Yes, but when you leap into the boxcar, you land on the train. The bird doesn't land on the train at all.

## #16 Re: Help Me ! » A bird flies into a train » 2011-10-12 02:47:46

When I try to post a link, I get this message:

Sorry. In an effort to stop automated spam only established members can post links. Please describe where instead.

www.qi.com/talk/viewtopic.php?t=22094&start=0

BTW, neither the poster nor the poster's friend is my friend. They're just members of that forum (of which I'm also a member). My conclusion is that the bird is stationary with respect to the train passengers, but the poster (Melonhead) doesn't agree, claiming that it's counterintuitive to see a bird flapping its wings like mad and still going nowhere.

## #17 Help Me ! » A bird flies into a train » 2011-10-12 01:40:06

Sylvia104
Replies: 19

This is a problem proposed by someone from another forum:

I have been having an ongoing disagreement with a friend about the outcome of a hypothetical situation involving a train and a bird. I'm hoping someone from this forum will be able to help me understand the physical laws that support my argument OR shoot me down in flames and tell me where Ive gone wrong.

Let's imagine that there is a train travelling North at a constant speed of 50mph. Outside, there is a bird flying parallel with the train that is also moving North at a constant speed of 50mph. (with me so far?). The bird then edges closer to the train and while still facing North the bird enters the train via a window.

I propose that once inside the train, assuming the bird continues to flap at its constant rate; it will fly towards the front of the train. Someone inside the train will observe the bird moving forward through the train at 50mph.

My friend proposes that the bird will stay at the same point in the train that it entered. I.e. if it entered at the back of coach E, even though its still flapping like mad, it will remain at the back of coach E and will appear stationary to an observer within the train.

What worries me is how blindingly obvious it seems to me that Im right. This feeling often coincides with me being wrong.

So who is right, the poster or their friend? I made some replies on that forum but it seems they were not being taken kindly to. I'd like to link you to the original discussion in the other forum but it seems I can't post links on this forum.

## #18 Re: This is Cool » Multiply 11 up to 19 (shortcut) » 2011-09-19 10:07:04

When I do mental calculations, I normally look for shortcuts, and different calculations often require different shortcuts. For 16 × 19:

And for 12 × 16:

## #19 Re: Help Me ! » normal subgroups » 2011-09-19 09:56:21

Let
. Then
is cyclic generated by a power of
, say
. Let
for some integer
, and
. Since
is normal in
, we have
for some
. Hence

as required.

## #20 Re: This is Cool » Inference! » 2011-09-19 08:18:22

When you pass from a statement or set of statements to a new statement by logical deduction, you are said to infer the new statement. Example:

(i) All dogs have four legs.
(ii) Rover is a dog.
(ii) Therefore Rover has four legs.

The last statement is an inference from the first two.

## #21 Re: Help Me ! » General linear algebra question » 2011-09-19 07:56:11

In the case of an
augmented matrix:

(1) if

then the system will not always be consistent (if consistent it will have infinitely many solutions),

(2) if

then it will be consistent (and its solution is unique),

(3) if

then it will also be consistent (but will have infinitely many solutions).

You're welcome.

## #23 Re: Help Me ! » axiomatization of real numbers » 2011-09-19 06:14:52

Apologies. If you substitute
in (+ 3) you only prove part of the theorem, namely that for all elements
there exists a unique
such that
. Let
be any other element, so there exists a unique
such that
. We need to show that
.

Now

to the first equation and
to the second equation. By using a combination of the commutative and associative axioms for addition, you should get

By uniqueness,

as required.

## #24 Re: Help Me ! » axiomatization of real numbers » 2011-09-19 05:25:07

jozou wrote:

Now following theorem holds: There is precisely one element (which will be denoted
), which is solution of equation
.
Proof: Assume some fixed
. Let the only solution of
be denoted by symbol
. So
holds.

Now proof is straightforward and I will not finish it.

The proof is incorrect. You are merely restating the theorem, not proving it. To prove the theorem, you just have to substitute
in axiom (+ 3).