Can someone define what a tuple is for me?

[Solid Snake]

Ok, so I read that a tuple is an ordered list of n elements, where n is a non-negative integer. Sometimes I get confused with tuples and partially ordered sets. So if I organized a list of all the airplanes in a particular airport, would that be a tuple, or would that be a set? I'm leaning towards it being a set, but by reading the definition of a tuple, I can also see it being a tuple. Other than a point in a graph, or a vector, where else in real life would I see something and say, "look, there's a tuple!". I would really want a clear definition in layman's terms so that I can be able to have these concepts clear in my mind, in particular the concept of a tuple.

 

[Simon Bridge]

The trick with tuples is that the position of the number in sequence has a meaning ... like the number 157 is a 3-tuple because the positions code hundreds, tens, and ones from left to right. The order has to be important ... like 1st, 2nd, 3rd ... i.e. a set of polygons could be described by a tuple where the nth entry in the list is the number of polygons with n sides in the set. If I draw the polygons from the set one at a time, then the sequence of polygons could be a tuple.
Ordered pairs are a list of 2-tuples in the order that they are to be drawn on a graph ... (x_i,y_i) if there are a finite number of them [edit: I am corrected, you cannot have an infinity-tuple] the position of the number in the list refers to a component of position on a graph.

In the end you define a mathematical object by it's list of properties ...
Distinguish from a set by:
1. $(1,2,3)\neq (3,2,1)$ while $\{1,2,3\} = \{3,2,1\}$
2. Multiple entries are allowed: $(1,1,3)$ would be a tuple from set $\{1,3\}$
3. Must have a finite number of elements.

So for the set of aircraft at an airport: organize by, say, weight, then that is just a sorted list. But if you have, say, 10 gates at the airport, then you can define a 10-tuple that stores the flight-number currently docked at each gate (0000 for empty gate, say). You could presumably define weight ranges so-many tonnes wide, and record the number of aircraft at the airport that fit in each weight range ... store that as a tuple. Similarly the top 3 heaviest aircraft would be a 3-tuple is the 1st position were heaviest etc. The names of the medal winners at an olympic event (if in a specific order each time) would be a 3-tuple like that.

It's unusual, in practise, that you actually care about the exact name of a mathematical structure like this though: you just use whatever seems appropriate at the time. Certainly not worth focussing on... this is probably the most I've used the word in a decade. The time the name becomes important is when you want to use someone elses result for a general property - in that case you realize the property and look up the name of the theorem that applies. (The other time is in an exam and you are specifically asked...) Thus: this is where I found out that I'm wrong ;)

 

[Solid Snake]

So for the set of aircraft at an airport: organize by, say, weight, then that is just a sorted list. But if you have, say, 10 gates at the airport, then you can define a 10-tuple that stores the flight-number currently docked at each gate (0000 for empty gate, say). You could presumably define weight ranges so-many tonnes wide, and record the number of aircraft at the airport that fit in each weight range ... store that as a tuple. Similarly the top 3 heaviest aircraft would be a 3-tuple is the 1st position were heaviest etc. The names of the medal winners at an olympic event (if in a specific order each time) would be a 3-tuple like that.

It's unusual, in practise, that you actually care about the exact name of a mathematical structure like this though: you just use whatever seems appropriate at the time. Certainly not worth focussing on... this is probably the most I've used the word in a decade. The time the name becomes important is when you want to use someone elses result for a general property - in that case you realize the property and look up the name of the theorem that applies. (The other time is in an exam and you are specifically asked...) Thus: this is where I found out that I'm wrong ;)

So just to make sure I understand you well, can I understand a tuple to be a list of data where each element is related to each other and ordered in that each index holds a value representing a specific thing?

Thank you so much for your reply.

 

[Simon Bridge]

The element position in the list should have meaning - the elements are related to each other in that they all appear on the list.
Examples of what I mean by the position in the list having meaning have been provided above: there is something special about being first, second, fifty-fourth or whatever on the list so that the order of the elements matters.

Imagine the kind of list where you number the entries ... a tuple is just such a list, only the numbers are implied by the position of the entry: #1 on the list is the 1st entry in the tuple.

Note: Everything is related to everything else in some way, though, usually, you don't bother making the list unless the elements are related in some way you find important.

 

[pbuk]

So if I organized a list of all the airplanes in a particular airport, would that be a tuple, or would that be a set? I'm leaning towards it being a set, but by reading the definition of a tuple, I can also see it being a tuple. Other than a point in a graph, or a vector, where else in real life would I see something and say, "look, there's a tuple!". I would really want a clear definition in layman's terms so that I can be able to have these concepts clear in my mind, in particular the concept of a tuple.

Using your example of an airport, a good example of a tuple would be (flight number, destination, departure time) or (flight number, date, seat number, passenger name).