The set is the basic object of set theory, which can be considered the underlying foundation of mathematics. Not much can be said about sets, other than that they may or may not contain elements, and that sets can be forms using certain set theoretic operations such as union and intersection.

One highlight of set theory is dealing with the celebrated Russell's Paradox.

A Finite or Infinite collection of objects in which neither order nor multiplicity has significance.

Set is a simple but interesting card game played with a deck of 81 cards. Each card has a group of symbols which represents one possible choice from the following set of options:

• Number: one, two, or three symbols
• Color: red, green, or purple
• Shape: ovals, diamonds, or squiggles
• Pattern: open, half-shaded, or solid

All 81 combinations are represented once each.

A set is a group of three cards which are either all the same or all different for each variable.

This game is among the best ways to blow 15 bucks. This game can be played anywhere with enough flat space to lay out the cards and with any number of participants - even alone.

Since the rules are so simple, the game crosses cultural and linguistic barriers; I played Set many a time in Japan with host families and students at my school. I can't explain the simple rule "If two are, and one isn't, then it's not a set" in Japanese, but I had the kids playing Set like a pro within 10 minutes.

It's not a CCG. Set can be played equally by 7-year-olds and 50-year-olds. Age is no advantage. Experience is only a minor advantage; I usually win the first two or three games, after that, things start evening out.

Set would make a lousy computer game; the computer could identify every set in a layout within microseconds. It would make a good (and simple!) network game, though, and probably could be implemented easily in Java by someone who knew what they were doing.

A collection of elements which can be proven to be completed by the axioms of set theory and the theorems that can be proven from them.

The collection of every object which meets a certain condition or predicate is not a set, it is a class. If you don't define things this way, you let youself in for A blather of paradoxes when infinite sets come into play. However, many classes are represented by sets. Indeed, most of set theory is dedicated to determining which (infinite) classes are represented by (infinite) sets.

Modern set theory contains no concept of an "individual element". In other words, the only things that can be elements of sets are other sets. This is quite a far cry from the set theory taught in first grade, built around collections of real objects!

The essential property of a set is elementhood. That is, a set (call it S) is described by saying something like: "This is in S. Also, this other thing is in S. Also everything in this other set is in S..."

The assertion that a certain set a is an element of another set b is symbolized

a ∈ b

or, for browsers that can't handle HTML character entities for mathematical symbols,

a e b

The definition of a set allows for no repetition of elements. A set is either a member of another set, or it is not.

Elementhood can be used to build more complex statements about sets:

a = b

"a equals b"

if every element of a is an element of b, and vice versa.

a <= b

a ⊆ b

"a is a subset of b"

if every element of a is an element of b.

a < b

a ⊂ b

"a is a proper subset of b"

if every element of a is an element of b, and a != b.

a U b

a ∪ b

"a union b"

is the set of all sets that are in a, b, or both.

a * b

a ∩ b

"a intersection b"

is the set of all sets that are in both a and b.

a^b

is the set of all mappings from a subset of a to a subset of b.

Set is a unique card game based on the mathematical concept of the set. You have a deck of normal size playing cards that has 81 cards in it. All of the cards are different. The idea is to get the most sets before there are no more sets. It is a very interesting game and has produced more than a few setaholics.

Here is a list of the rules:

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Rules

The object of the game is to identify a 'Set' of three cards from 12 cards laid out on the table. Each card has a variation of the following four features:

(A) COLOR:

Each card is red, green, or purple.

(B) SYMBOL:

Each card contains ovals, squiggles, or diamonds.

(C) NUMBER:

Each card has one, two, or three symbols.

(D) SHADING:

Each card is solid, open, or striped.

A 'Set' consists of three cards in which each feature is EITHER the same on each card OR is different on each card. That is to say, any feature in the 'Set' of three cards is either common to all three cards or is different on each card.

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The Magic Rule

If two are... and one is not, then it is not a 'Set'.

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The Play

The dealer shuffles the cards and lays twelve cards (in a rectangle) face up on the table so that they can be seen by all players. The players remove a 'Set' of three cards as they are seen. Each 'Set' is checked by the other players. If correct, the 'Set' is kept by the player and the dealer replaces the three cards with three from the deck. Players do not take turns but pick up 'Sets' as soon as they see them. A player must call 'Set' before picking up the cards. After a player has called 'Set', no other player can pick up cards until the first player is finished. If a player calls 'Set' and does not have one, the player loses one point. The three cards are returned to the table.

If all players agree that there is no 'Set' in the twelve cards showing, three more cards (making a total of fifteen) are laid face up. These cards are not replaced when the next 'Set' is picked up, reducing the number to twelve again. If solitaire is being played, the player loses at this point.

The play continues until the deck is depleted. At the end of the play there may be six or nine cards which do not form a 'Set'.

The number of 'Sets' held by each player are then counted, one point is given for each and added to their score. The deal then passes to the person on the dealer's left and the play resumes with the deck being reshuffled.

When all players have dealt, the game ends; the highest score wins.

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NOTE: If you are playing with color blind people, you will need to mark either the red or the green cards to make it easier for them to play the game.

SET (Secure Electronic Transaction, from SET Secure Electronic Transaction LLC) is also one method of sending credit card information over the Internet securely, using strong encryption.

I can only comment on Finnish side here: Luottokunta (the credit card corporation responsible for VISA and Mastercard in Finland) specifically told people not to send credit card information to the shop over the Internet - instead, they recommended snail mail, phone or fax, which was pretty strange because faxes and telephone lines in general are less secure than PGP or even the 40-bit SSL that was used at that time.

They chose SET for this, but it never caught on - I heard it was pain to implement at server, so only few shops in the end decided to use SET. Furthermore, the SET client was only available for Windows. Currently, Luottokunta approves the use of SSL, too.

In theatre, the created location in which the play takes place. This can be anything from a bare stage to a plumbed and wired functional house to an existing location used as the setting for the play. The set is envisioned and created by the set designer in collaboration with the director and realized by the technical director and his crew of carpenters, welders and painters.

The legends surrounding Set are many, and even his description varies from the form of a serpent, an aardvark-headed man or even a greyhound. What he symbolizes is also a matter of some dispute, as some believe it is chaos, others claim outright evil, while many Egyptologists cling to the idea that he is the deity of iron. In many myths, Set is portrayed as the brother of Osiris, which in turn leads to the bizarre account of Set's murder of his brother. Stories surrounding this fratricide range from the intense[ to the [mild, going so far as to speak of dismemberment and rape of the corpse of Osiris. Within the Book of the Dead, Set is said to be "the great northern sky", responsible for cloudy skies and stormy weather. In the Book, is said to protect the sun god Re on his nightly voyage through the underworld. The cult of Set finds significance in the Desert Oryx, crocodile, boar, and hippopotamus, in that they are all destroyers of field and boat.

Set: An Introduction To The Idea Of Geometry In Four Dimensions

Believe it or not, the simple card game of set is actually based on four dimensional geometry. No really. And you thought it was just a waste of time...

For those of you who haven't played it, set is played with 81 cards, as described by /dev/joe above. Now 81 = 3⁴ = 3x3x3x3, which is no coincidence - but you'll see why this is later, if you haven't already.

To play, you lay 12 cards out on the table, and the players have to find a set, which is a collection of three cards from the 12, where for each category (colour, number, shape or pattern), either they are all the same (for example, all three are red) or they are all different (one is diamonds, one ovals and one squiggles). And to make a set, you have to do this for all categories at once.

So the triplets that aren't sets are the ones where two are red and one is blue, or two are half-shaded and one is solid, or two have one symbol and one has three - you get the idea.

When you find a set, you yell "Set!", show the set to the other players to check that it actually is a set, and then keep those cards. Then the dealer deals three more cards to bring the total back to 12 on the table. If nobody can find a set from the 12 on the table, another 3 cards are dealt out to help, giving 15 to choose from (although even then it's not always possible to find a set - I'll come back to this).

The idea is very simple - the person with the most sets at the end of the game wins.

Now believe it or not, you can think of the cards in Set as points on a four-dimensional grid, and the sets as lines in the grid.

I'll demonstrate with a simplified game.

Suppose you just had two categories: colour and shape. Your cards are either red, blue or green, and they either have ovals, diamonds or squiggles on - you have 9 cards. Now, suppose you draw a graph with shape down one axis, and colour down the other; then you could put each card into its place in on the graph, and so arrange them in a 3x3 grid.

Here's where it gets nice: the sets in the game of Set are just the lines on the grid - the places where you have to get three in a row to win at tic-tac-toe. There are eight possible sets: three lines of same shape different colour, three lines of same colour different shape, and two diagonals which correspond to sets which share neither colour nor shape.

Now we can add in the possibility of different numbers, and so add an extra axis on our graph. We now get a 3x3x3 grid, like a three-dimensional tic-tac-toe board; the sets are still the lines on the grid, although now there are a lot more possibilities.

Lastly, we add a pattern axis into a hypothetical fourth dimension, making a 3x3x3x3 grid. Now here's where it starts to get difficult to visualize, but that doesn't really matter, because everything works basically the same as the three-dimensional case.

I'll expand on that idea. Suppose you have just one category; let's say shape. Your cards are all red, and have one symbol and are solid shaded, but one's oval, one's squiggly and one's a diamond. Then you'd have three cards arranged in a line. To add colour, you do the following: make two copies of the line of cards, one in blue and one in green. Then lay both copies alongside the first one, and voila! A 3x3 grid with both categories.

Likewise, to add shading, you make two copies of the 3x3 grid, one half-shaded and one unfilled, and lay them next to the first one to make a 3x3x3 grid.

So when you get to a 3x3x3x3 grid, it's not really too hard to think of - you just make two copies of the 3x3x3 grid, with different numbers of symbols on each card, and lay them alongside the first one. You can think of this happening in three dimensions without too much difficulty, although it's not so easy to work with.

You've probably heard of Einstein's theories that the world is four dimensional and time is the fourth dimension, but don't worry about that for now - just think of the fourth dimension as being the same as the first three; as well as up/down, left/right, forwards/backward, you get another direction to go to.

This is how mathematicians and physicists deal with spaces that have more than three dimensions - start small, and work up.

And what's more, even with four dimensions, the sets are still the lines where you would win at tic-tac-toe (although you wouldn't play tic-tac-toe on a 3d or 4d grid, because the first player would always win - but that's another story). It's not entirely obvious why this is, but if you think about it you should be able to convince yourself.

One interesting fact that comes out of all this is that it's possible to have 16 cards on the table without there being a set there - just take any 2x2x2x2 block from the 3x3x3x3 grid, and it can't have any full lines. On the other hand, if there are 17 or more cards on the table, then there has to be a set in there somewhere. I don't think I've ever seen more than 15 cards dealt, but in theory it could happen.

So far, my geometric ideas about the game of set haven't helped me win (:-(), but I'm gonna keep trying - this game is just way to addictive.

Set (or Seth) was the Egyptian god of evil, patron of mayhem, war and natural disasters. He loved the sound of tearing flesh; the wolf and the hyena were his creatures. Though brother to Orisis, most divine and beautiful of the gods, Set himself displayed an alien ugliness. His skin was an unhealthy white, in stark contrast to the warm honey and ebony tones of his brethren, and his hair was a startling red, the color of evil.

Jealous of his brothers rule (with his sorceress queen,and sister as was the custom of the pharaoh's, Isis at his side) Set tricked Orisis into a deadly trap, by way of an ornate coffin. In time Isis restored her husband to life, and their son Horus was raised in preparation to challenge his uncle.

Through ceaseless and uncertain battles, the forces of Set and Horus waged war for the right of soverignty over Egypt. The throne was eventually handed to Horus by way of a trial, judged by Thoth-lord of the moon, said to have lasted eighty years.

Here differences arise, Some tales claim that Set was banished to the desert, while others that he was forever forced into the role of the servant - guarding the shining ship of Ra.

"A set" is a term used to describe a poker hand more commonly called three-of-a-kind or trips, usually heard while playing the game Texas Hold-Em.

The most common scenerio when this occurs is when a player has starting (or hole) cards that are of the same rank (a pair) and then the one of the "community cards" (or board) matches the paired hole cards.

 

In the poker game Texas Hold 'Em (and probably other games with community cards,) a set is a three of a kind hand composed of one community card and a pocket pair, that is, two pocket cards of the same rank. It differs