Are tuples ordered pairs?

Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Alternatively, the objects are called the first and second components, the first and second coordinates, or the left and right projections of the ordered pair.

What is ordered pair in math?

An ordered pair is a pair of numbers, (x,y) , written in a particular order. The ordered pair (x,y) is not the same ordered pair as (y,x) .

What is an ordered pair of elements?

An ordered pair consists of two numbers that are written in the fixed order. So, we can define an ordered pair as the pair of elements that occur in a particular order and are enclosed in brackets.

Can we multiply two sets?

For two non-empty sets (say A & B), the first element of the pair is from one set A and the second element is taken from the second set B. The collection of all such pairs gives us a Cartesian product. Cartesian product A×B = {(a1,b1), (a1,b2), (a1,b3), ( a2,b1), (a2,b2),(a2,b3), (a3,b1), (a3,b2), (a3,b3)}.

How to extract the first and second element of a tuple?

As you might guess, a two element tuple is commonly called a “pair” and a three element tuple is called a “triple” and so on. In the special case of pairs, there are functions fst and snd which extract the first and second element. They only work on pairs. Trying to use fst on a triple will give an error.

Why do we convert a tuple to an array?

Explanation: arrays make direct scalar multiplication possible. Hence the tuple called set1 here is converted to an array. I assume you wish to keep using the tuple, hence we convert the array back to a tuple. This solution is to avoid the explicit and verbose for loop.

How do I compare two tuples?

Tuples have an automatically defined equality operation: two tuples are equal if they have the same length and the values in each slot are equal. Trying to compare tuples of different lengths is a type error:

What is the definition of multiplication of ordered pairs?

There are many ways to define multiplication of ordered pairs, and the one you use depends on what you’re using it for. Multiplication is an operation that occurs in monoids, groups, rings, and other algebraic objects. The most common definition is to define multiplication coordinatewise.