What is Ordinal Numbers, Why Everyone is talking about it, It's real-world Application:

(In Simple Words)

In mathematics, "ordinal numbers" are a type of number used to describe the order of things. They are a generalization of the idea of "first, second, third, etc." that we use to count things in everyday life.

The goal of ordinal numbers is to help us understand and describe the order of infinite sets, which are sets that have an unlimited number of elements. For example, the set of all positive integers (1, 2, 3, 4, and so on) is an infinite set.

Ordinal numbers provide a way of labeling the elements in an infinite set in a specific order. For example, we can use ordinal numbers to label the elements of the set of positive integers as "first", "second", "third", and so on, even though the set has an unlimited number of elements.

So in simple terms, ordinal numbers are a type of mathematical number used to describe the order of infinite sets, in a similar way that we use "first", "second", "third", and so on, to describe the order of things in everyday life.

Why should we care about it:

Ordinal numbers play an important role in many areas of mathematics, including set theory, topology, and algebra. Understanding ordinal numbers can be useful for understanding a wide range of mathematical concepts and for solving mathematical problems.

One reason why ordinal numbers are important is because they provide a way to describe and understand the order of infinite sets. By labeling the elements of an infinite set in a specific order, we can gain a better understanding of the set as a whole and its properties.

Another reason why ordinal numbers are important is because they provide a foundation for the study of other mathematical concepts, such as cardinality and well-ordered sets. Cardinality is a measure of the size of a set, while well-ordered sets are sets that have a specific order that allows us to compare the elements of the set. Understanding ordinal numbers can help us understand these other mathematical concepts.

In addition, ordinal numbers are used in many practical applications, such as computer science, where they are used to describe the order of algorithms and data structures.

So overall, understanding ordinal numbers is important for a deeper understanding of mathematics and for solving mathematical problems. It also has practical applications in areas such as computer science and can be useful for solving real-world problems.

Its Real-world Application:

Ordinal numbers can be applied to a variety of real-world problems, particularly in computer science and engineering. Some examples include:

1: Algorithm analysis: Ordinal numbers can be used to describe the order of algorithms, which are sets of instructions used to solve a specific problem. By using ordinal numbers, computer scientists can analyze the efficiency of algorithms and determine the best algorithm to use for a specific problem.

2: Data structures: Ordinal numbers can be used to describe the order of elements in data structures, such as linked lists, trees, and graphs. By understanding the order of elements in a data structure, computer scientists can design algorithms that can efficiently search, sort, and manipulate the data.

3: Decision making: Ordinal numbers can be used in decision making problems, such as voting systems and preference ranking. For example, in a voting system, ordinal numbers can be used to rank the preferences of different voters and determine the most preferred option.

4: Resource allocation: Ordinal numbers can be used to prioritize and allocate resources, such as in project management and scheduling. For example, a project manager might use ordinal numbers to rank tasks based on their importance and allocate resources accordingly.

These are just a few examples of the many real-world problems that ordinal numbers can help solve. By providing a way to describe and understand the order of things, ordinal numbers can be applied to a wide range of problems in computer science, engineering, and other fields.

If you want to read it later: https://iefan.substack.com/p/what-is-ordinal-numbers-in-simple?sd=pf

Or if you want to take a deep dive: https://en.wikipedia.org/wiki/Ordinal_number?wprov=sfla1