# BBO Discussion Forums: Question and Answer thread - BBO Discussion Forums

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### #41kenberg

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Posted 2011-March-22, 07:39

The generic term is fixed point. Suppose that X is some set, it matters not at all what sort of set. Suppose f is a function such that for each x in the set X, f(x) is also some point of X. In shorthand f:X->X. Then: If f(x)=x then x is called a fixed point for the function f.

For whatever interest it may hold, here is one of the more famous fixed point theorems (called the Brouwer Fixed Point Theorem although the pedigree is maybe more complicated): If X is any closed ball of any (finite) dimension and f: X->X is continuous then f has a fixed point. "Closed" means that the boundary points of X are included in X.

A closed 1-dimensional "ball" is just a closed interval, in 2 dimensions it's a disk, in 3 dimensions it is what you really think of as a ball, and mathematically you can have any number of dimensions.

As for usefulness, it can be in the eye of the beholder. If you take any one theorem from mathematics, by itself it is apt to have little use. As a collective body of knowledge and as a way of dealing with very practical problems, it would be an error to dismiss even the most theoretical mathematics. For a well-known example, the success of the Google search engine was based in part on theorems in linear algebra. See http://www.rose-hulm...ersionFixed.pdf

Similarly, the Brouwer Fixed Point Theorem, and a flock of other fixed point theorems, have been very useful in the right hands, applied to the right problems. Think Nash Equilibrium, see http://en.wikipedia....ash_equilibrium
Ken
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### #42mycroft

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Posted 2011-March-22, 10:08

Ah, good, thanks. I'm glad I was thinking clearly that there was a use for defining a term for that property.

I like the "stupid things you can do with n-dimensional spheres" stuff, too. The worst of those was wrapping my head around "the entire volume of an infinite-dimensional sphere is on its surface" - even with the math that proved it. I've been able to be comfortable with some of "things are different at infinity/infinitesimal", but that one broke my brain for a couple of weeks.

And you don't need to prove to me that there is a use for pure math - I did a degree in cryptography, after all, and had to learn matroid theory the hard way to understand secret sharing schemes (I loved the way that developed in the literature, too: the engineer/applied mathematician/"S" in RSA found a cool development of field theory that allowed for zero-Shannon-information if n-1 people pooled their data, but 100% recovery if one more did (for any people); then they found that they could do "these two people, or any three"; then a mathematician showed that this was a matroid, which exploded the solved space in a very short time: "since it's a matroid, we can do <this>, which means that <this real-world problem> is solvable, and it can be generalized to <that>"; and now the engineering people (like me) were playing catchup).
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### #43gwnn

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Posted 2011-April-08, 06:53

I have some pdf format books (some of them maybe copyrighted - don't tell anyone). Sometimes I lose track of where I last was. Is there an easy way of doing this or should I just open a text document on the side?
... and I can prove it with my usual, flawless logic.
George Carlin
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### #44655321

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Posted 2011-April-08, 16:33

gwnn, on 2011-April-08, 06:53, said:

I have some pdf format books (some of them maybe copyrighted - don't tell anyone). Sometimes I lose track of where I last was. Is there an easy way of doing this or should I just open a text document on the side?

Probably eReaders will remember your place - I tried it with Bluefire on the iPad and it works.
That's impossible. No one can give more than one hundred percent. By definition that is the most anyone can give.
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### #45matmat

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Posted 2011-April-09, 22:10

If you're using an do*be product to read the pdfs, your version might have a bookmark feature; you do have to save the modified pdf afterward, however.
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### #46Foxx

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Posted 2011-April-16, 00:30

OK, this is going to sound a little odd, but can anyone identify the kinds of wood shown in this picture:

#### Attached File(s)

•  wood.jpg (33.15K)

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### #47matmat

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Posted 2011-April-23, 14:53

Foxx, on 2011-April-16, 00:30, said:

OK, this is going to sound a little odd, but can anyone identify the kinds of wood shown in this picture:

For some reason I can't read the attachment
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### #48gwnn

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Posted 2012-March-07, 06:34

I am reading about s-trans-1,3-butadiene. I know what trans-1,3-butadiene means, but what is the s? I am a complete chemistry moron. I would guess it's got something with s orbitals?! Googling didn't bring much joy. It seems they always use "s-trans".
... and I can prove it with my usual, flawless logic.
George Carlin
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### #49helene_t

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Posted 2012-March-07, 06:41

s for "single bond". http://www.chem.ucla.../S/s_trans.html
A simple tinfoil hat should suffice. Then the computer won't be able to read his brainwaves to tell which way he's going to take 2-way finesses, and move the queen behind it. --- barmar
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### #50gwnn

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Posted 2012-March-07, 06:46

well it is a weird nomenclature but ok, I should have found that!
... and I can prove it with my usual, flawless logic.
George Carlin
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### #51onoway

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Posted 2012-March-07, 17:43

Foxx, on 2011-April-16, 00:30, said:

OK, this is going to sound a little odd, but can anyone identify the kinds of wood shown in this picture:

If you haven't already done so, you might check out the places that carry veneer wood. This place has very nice photos of veneer wood so maybe you would find a match if you browsed through it
http://www.woodveneer.com/veneer.html There are also other such sites. Good luck.
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### #52mgoetze

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Posted 2012-March-07, 18:57

kenberg, on 2011-March-22, 07:39, said:

If X is any closed ball of any (finite) dimension and f: X->X is continuous then f has a fixed point.

In my mind this statement immediately raised the question of whether this is true for any given topology, but Wikipedia was able to answer that easily so I guess it is off-topic for this thread.
"One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision"
-- Bertrand Russell
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### #53Cyberyeti

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Posted 2012-March-07, 18:58

helene_t, on 2012-March-07, 06:41, said:

The s seems to be superfluous. I can see that buta 1,3 diene can be trans or cis, but what's the alternative to "s". I didn't see this terminology in the UK when I was doing chemistry as an undergrad 25-30 years ago.
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### #54gwnn

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Posted 2012-March-08, 00:41

Cyberyeti, on 2012-March-07, 18:58, said:

The s seems to be superfluous. I can see that buta 1,3 diene can be trans or cis, but what's the alternative to "s". I didn't see this terminology in the UK when I was doing chemistry as an undergrad 25-30 years ago.

It is superfluous, but maybe it is neater to have the same term apply for all cis/trans isomers around a single bond? I don't know.
... and I can prove it with my usual, flawless logic.
George Carlin
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### #55JLOGIC

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Posted 2012-March-08, 01:30

Wolfram Alpha + Quora + Google, you shouldn't need anything else.
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