Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
She's sleeping now, with a smile on her face.
I wasn't the only one smiling, Slut.
I love you.
I wasn't the only one smiling, Slut.
I love you.
vella_ms
Literotica Guru
- Joined
- Apr 27, 2008
- Posts
- 539
I wasn't the only one smiling, Slut.
I love you.
hot damn! i love the word slut...only second to slag.
Trombonus
A bit older, a lot wiser.
- Joined
- Jul 17, 2006
- Posts
- 15,398
hot damn! i love the word slut...only second to slag.
Slag was my favorite Dinobot for the longest time, but I like Snarl better now. Funny, because in Transformers Animated they have a Dinobot modeled after Slag, but named him Snarl (due to trademark issues).
Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
Are you so strong, or is all the weakness in me?
Safe_Bet
No she's not back I'm Amy
- Joined
- Aug 6, 2008
- Posts
- 8,663
Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
Have I rode the days and nights on rails, to get back where you are?
Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
There's more than one answer to these questions . . . pointing me in a crooked line. And the less I seek my source for some definitive, the closer I am to fine.
Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
Everything reminds me . . . music surging bedroom dance . . . crazy spinning sultry glance. I inhale your presence still . . . these your arms of daring grace encircle me - what pact is made. Desire is your masquerade.
Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
Keep your drink . . . just gimme the money . . .
TheeGoatPig
There is no R in my name
- Joined
- Dec 29, 2004
- Posts
- 13,163
ABSTRUSE
Cirque du Freak
- Joined
- Mar 4, 2003
- Posts
- 50,094
ABSTRUSE
Cirque du Freak
- Joined
- Mar 4, 2003
- Posts
- 50,094
Reconnected with a dear old friend. Never realized how much I missed her.
I hope to get to NYC to meet her.
we were suppossed to go to art school together, she went to Pratt and I went to Hell...I mean Marywood.
She's a success now.
I'm shit.
I hope to get to NYC to meet her.
we were suppossed to go to art school together, she went to Pratt and I went to Hell...I mean Marywood.
She's a success now.
I'm shit.
DesertPirate
Sailing from the desert
- Joined
- Mar 20, 2006
- Posts
- 20,432
You are not shit!
You are a good friend and helpful to all.
Nirvanadragones
Literotica Guru
- Joined
- Sep 9, 2005
- Posts
- 14,399
if words were more her medium than touch
near you is one frighteningly real who cannot plan
whose heart's a cat from which
your habits dart like birds
who had no weight until you gave
false lust and words like "lost"
a chance to twist my body into complicated shapes.
near you is one frighteningly real who cannot plan
whose heart's a cat from which
your habits dart like birds
who had no weight until you gave
false lust and words like "lost"
a chance to twist my body into complicated shapes.
MagicaPractica
Alchemist
- Joined
- Oct 25, 2004
- Posts
- 20,069
There are always two sides to every situation. I think this is often why relationships fail, because one, or both, fail to really say what they mean and/or listen to the other person. Lines of communication break down, or aren't built to begin with. The whole thing leaves confusion and a lack of resolution in it's wake. Trying to make sense of it seems to go nowhere.
cloudy
Alabama Slammer
- Joined
- Mar 23, 2004
- Posts
- 37,997
Not always, but then there's those...moments, those stellar seconds that make you keep trying, yes?
mynameisben
Half man, half-wit
- Joined
- Apr 18, 2003
- Posts
- 50,217
Set Theory is a branch of mathematics which, on its surface, is very intuitive. Its fundamental precepts have been taught in grade schools for decades. Since most of us here are decades removed from grade school, a brief refresher on this refreshingly computation-free side street of mathematics may be in order. The refresher I now give may be a bit dry, but I encourage you to hang with it because what follows is actually quite interesting. For those of you who are already well versed in the basics of set theory (and for those who are currently in grade school), feel free to skip ahead to the section marked, "Now Things Get Interesting!"
Whirlwind Set Theory Refresher
A set is a grouping of "things" called elements (also called "members"). An element is typically a number, but an element may also be any "thing" at all. An apple, Richard Nixon, and the number 43 are all examples of elements that may be included as the members of a set. Don't get confused. Element, member, and item mean pretty much the same thing.
Conceptually, a set may be thought of as a bag or any container into which you may place elements (things). Notationally, a set is a list of items that are separated by commas, and the entire list is surrounded by curly braces. Think of the curly braces as the fabric of the bag itself.
For example,
{1, 2, 3, 4}
is a set containing four elements, which are the first four positive integers. Set, container, group, and bag mean pretty much the same thing, too. This is all very intuitive stuff we're talking about here.
Mathematicians assign names to sets so that sets may be conveniently identified for discussion. The naming of sets is shown symbolically as a variable (usually a single letter of the alphabet), followed by the equals sign, followed by the set itself.
A = {1, 2, 3, 4}
B = {apple, orange, banana}
C = {Richard Nixon}
D = { }
are four examples of sets, named A, B, C, and D. Note that set D contains no elements at all. A set with no elements is called the "empty set", which may be thought of as an empty bag that hasn't had anything put into it yet.
Mathematicians may be long winded at times, but they are also known to take shortcuts. If they want to describe a set that has a large number of elements, such as all the letters of the English alphabet, they would typically do something like this:
E = {all letters of the English alphabet}
rather than doing something much more tedious, like this:
E = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}
Such a shortcut may be handy for notationally describing sets with a large number of elements, but it is absolutely essential for describing sets which contain an infinite number of elements. A set which contains an infinite number of elements is called an infinite set.The idea of infinite sets strains our analogy of a set as a bag, but stay with it. In math world, bags are infinitely stretchy. Here are two examples of infinite sets:
F = {All numbers greater than zero}
G = {all possible sets}
The example of G = {all possible sets} is tricky, because it shows that a set can be an element of another set. A set is a "thing," so why not? It is okay, and Set Theory allows it. After all, it is entirely possible to place a bag within a bag. We do it all the time when we compartmentalize things. A desk may be thought of as a set. A desk is a container (a bag, essentially), which has drawer-1, drawer-2, and drawer-3 as it's three elements. Each of the three drawers is itself a set, because drawers are containers (bags) for other items (elements). Drawer-1 may contain a pencil, a pen, and an eraser. Drawer-2 may contain an envelope and a stamp, and Drawer-3 may be completely empty. A Set Theorist would describe the items of interest in such a desk thusly:
H = { {pencil, pen, eraser}, {envelope, stamp}, { } }
which shows set H (i.e.,the desk) consisting of three elements that are other sets (i.e., the drawers), the third set of which is the empty set.
There is much more to Set Theory than what has been described in this whirlwind tour, but it is enough background to move on to something more thought provoking and fun. Ready?
Now Things Get Interesting!
Since sets may include other sets, even infinite sets, it raises an interesting question or two. Can a set include itself as one of its members? Consider the following set:
J = {all sets of things that are not Richard Nixon}
Since J is a set, it is clearly not Richard Nixon. Set J, however, is a "thing," because a set is a thing. Therefore, the set J may be included as a member of itself. A set with the property that it contains itself as one of its own members is called a "self-swallowing" set. It's like the legendary Klein bottle, a bag that wraps itself around itself, a conceptual monstrosity that should rightfully vanish into a black hole of mathematical illogic. And yet it somehow persists.
J is a rather ugly set that people who cherish their sanity prefer to distance themselves from. In that spirit, let's get as far away from J as possible and consider another set:
K = {all sets that are not members of themselves}
Set K surely ought to safeguard our sanity. But think again! By some order of black magic, it can be mathematically demonstrated that set K is neither a member of itself nor NOT a member of itself!
If you're having difficulty wrapping your head around sets J and K, you are not alone. These maddening paradoxes rocked Set Theory to its very foundations just over a century ago. It forced mathematicians to admit that, for a brief while, they had been blithering in the ether. Google for "Russell's Paradox" if you are interested. Then look for Godel's Incompleteness Theorem if you really want the wind beaten out of your faith in mathematics. In a nutshell, Godel's theorem PROVES that "Any consistent, axiomatically defined system of mathematics necessarily contains propositions that can never be proven." This theorem is one of the propositions that has been legitimately proven. It applies to the algebra we all use and adore every day, not to mention the multidimensional hyper-galaxy algerbras so abstract they make a Salvador Dahli painting look like my AV. Godel is not saying that mathematics is inherently contradictory and should therefore be tossed onto the junk heap of perpetual motion machines and cold fusion. He's just saying that math is a wee more complex than most people ever begin to imagine.
And it drives home the point that one must always question one's sources. And that absolute truth, even in mathematics, is a slippery eel.
Whirlwind Set Theory Refresher
A set is a grouping of "things" called elements (also called "members"). An element is typically a number, but an element may also be any "thing" at all. An apple, Richard Nixon, and the number 43 are all examples of elements that may be included as the members of a set. Don't get confused. Element, member, and item mean pretty much the same thing.
Conceptually, a set may be thought of as a bag or any container into which you may place elements (things). Notationally, a set is a list of items that are separated by commas, and the entire list is surrounded by curly braces. Think of the curly braces as the fabric of the bag itself.
For example,
{1, 2, 3, 4}
is a set containing four elements, which are the first four positive integers. Set, container, group, and bag mean pretty much the same thing, too. This is all very intuitive stuff we're talking about here.
Mathematicians assign names to sets so that sets may be conveniently identified for discussion. The naming of sets is shown symbolically as a variable (usually a single letter of the alphabet), followed by the equals sign, followed by the set itself.
A = {1, 2, 3, 4}
B = {apple, orange, banana}
C = {Richard Nixon}
D = { }
are four examples of sets, named A, B, C, and D. Note that set D contains no elements at all. A set with no elements is called the "empty set", which may be thought of as an empty bag that hasn't had anything put into it yet.
Mathematicians may be long winded at times, but they are also known to take shortcuts. If they want to describe a set that has a large number of elements, such as all the letters of the English alphabet, they would typically do something like this:
E = {all letters of the English alphabet}
rather than doing something much more tedious, like this:
E = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}
Such a shortcut may be handy for notationally describing sets with a large number of elements, but it is absolutely essential for describing sets which contain an infinite number of elements. A set which contains an infinite number of elements is called an infinite set.The idea of infinite sets strains our analogy of a set as a bag, but stay with it. In math world, bags are infinitely stretchy. Here are two examples of infinite sets:
F = {All numbers greater than zero}
G = {all possible sets}
The example of G = {all possible sets} is tricky, because it shows that a set can be an element of another set. A set is a "thing," so why not? It is okay, and Set Theory allows it. After all, it is entirely possible to place a bag within a bag. We do it all the time when we compartmentalize things. A desk may be thought of as a set. A desk is a container (a bag, essentially), which has drawer-1, drawer-2, and drawer-3 as it's three elements. Each of the three drawers is itself a set, because drawers are containers (bags) for other items (elements). Drawer-1 may contain a pencil, a pen, and an eraser. Drawer-2 may contain an envelope and a stamp, and Drawer-3 may be completely empty. A Set Theorist would describe the items of interest in such a desk thusly:
H = { {pencil, pen, eraser}, {envelope, stamp}, { } }
which shows set H (i.e.,the desk) consisting of three elements that are other sets (i.e., the drawers), the third set of which is the empty set.
There is much more to Set Theory than what has been described in this whirlwind tour, but it is enough background to move on to something more thought provoking and fun. Ready?
Now Things Get Interesting!
Since sets may include other sets, even infinite sets, it raises an interesting question or two. Can a set include itself as one of its members? Consider the following set:
J = {all sets of things that are not Richard Nixon}
Since J is a set, it is clearly not Richard Nixon. Set J, however, is a "thing," because a set is a thing. Therefore, the set J may be included as a member of itself. A set with the property that it contains itself as one of its own members is called a "self-swallowing" set. It's like the legendary Klein bottle, a bag that wraps itself around itself, a conceptual monstrosity that should rightfully vanish into a black hole of mathematical illogic. And yet it somehow persists.
J is a rather ugly set that people who cherish their sanity prefer to distance themselves from. In that spirit, let's get as far away from J as possible and consider another set:
K = {all sets that are not members of themselves}
Set K surely ought to safeguard our sanity. But think again! By some order of black magic, it can be mathematically demonstrated that set K is neither a member of itself nor NOT a member of itself!
If you're having difficulty wrapping your head around sets J and K, you are not alone. These maddening paradoxes rocked Set Theory to its very foundations just over a century ago. It forced mathematicians to admit that, for a brief while, they had been blithering in the ether. Google for "Russell's Paradox" if you are interested. Then look for Godel's Incompleteness Theorem if you really want the wind beaten out of your faith in mathematics. In a nutshell, Godel's theorem PROVES that "Any consistent, axiomatically defined system of mathematics necessarily contains propositions that can never be proven." This theorem is one of the propositions that has been legitimately proven. It applies to the algebra we all use and adore every day, not to mention the multidimensional hyper-galaxy algerbras so abstract they make a Salvador Dahli painting look like my AV. Godel is not saying that mathematics is inherently contradictory and should therefore be tossed onto the junk heap of perpetual motion machines and cold fusion. He's just saying that math is a wee more complex than most people ever begin to imagine.
And it drives home the point that one must always question one's sources. And that absolute truth, even in mathematics, is a slippery eel.
Verdad
Literotica Guru
- Joined
- Sep 17, 2006
- Posts
- 1,430
Funny you should mention this just now, Ben. I read Logicomix just this week—a recent graphic novel bio of Bertrand Russell. It takes some liberties with fictionalizing Russell's life and the lives of the other participants, and it does not try to be a crash course in math, but it's not bad for giving one a quick idea about the search for foundations these guys had embarked upon. I'd recommend it to those readers who aren't very interested but would like to get a minimal handle in a cute wrapping.
mynameisben
Half man, half-wit
- Joined
- Apr 18, 2003
- Posts
- 50,217
Hey! That sounds like a really cool book. I can't wait to add it to my library.
Thanks for the link!
Thanks for the link!
Handley_Page
Draco interdum Vincit
- Joined
- Aug 18, 2007
- Posts
- 78,287
Thank YOU for the whirlwind tour.
I thought I saw elements of C and Unix in there for a moment.
mynameisben
Half man, half-wit
- Joined
- Apr 18, 2003
- Posts
- 50,217
/* You're welcome. */
/* Even though I have no idea what you are talking about. */
Handley_Page
Draco interdum Vincit
- Joined
- Aug 18, 2007
- Posts
- 78,287
*/ why don't I believe you ? /*
Verdad
Literotica Guru
- Joined
- Sep 17, 2006
- Posts
- 1,430
It's not deep on the exposition of the ideas, mind you, nor for that matter, the psychology of the characters, but it's not bad as a geeky-fun item. 
Similar threads
