Well-Defined Sets: Examples & Real World Use

[Kristinanne]

Homework Statement

Describe what it means for a set to be well defined and then give an example of a well defined set and an example of a set that isn’t well defined. Explain why it is so important for sets used in the real world, for example in marketing research, to be well defined.

Homework Equations

The Attempt at a Solution

A well defined set is clear without question. I am just unsure of how to use that in real life examples. Same with the one that isn't well defined.

 

[mutton]

Maybe the set of all people currently living on Earth who like ice cream is not well-defined because there are people who neither like nor dislike it, people who like some flavours but dislike others, people who don't know what ice cream is, etc. This is a problem if you want to survey what percentage of people like ice cream, so you have to clearly specify the subset you are looking at.

You can think of better examples.

 

[Architeuthis Dux]

A well defined set is a collection of objects that has a clear and unambiguous definition. This means that each object in the set must have a specific characteristic or property that distinguishes it from other objects, and that there is no ambiguity or confusion about what is included in the set.

An example of a well defined set would be the set of all prime numbers less than 10. This set includes the numbers 2, 3, 5, and 7, and each of these numbers has the specific property of being divisible only by itself and 1. There is no confusion about what numbers are included in this set, making it well defined.

On the other hand, an example of a set that is not well defined would be the set of "tall buildings." This set is not well defined because the term "tall" is subjective and can vary depending on individual perceptions. One person may consider a building over 50 stories tall to be "tall," while another person may consider a building over 100 stories tall to be "tall."

It is important for sets used in the real world, such as in marketing research, to be well defined because they provide clear and unambiguous criteria for categorizing and analyzing data. This helps to ensure that the data collected is accurate and reliable, and allows for consistent and meaningful comparisons to be made. In the example of marketing research, a well defined set of target customers would help a company to effectively target and tailor their marketing strategies, leading to more successful outcomes.