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Chapter 0: Problem 4

List the elements in each set. $$ \\{m \mid m \text { is a natural number less than } 9\\} $$

Short Answer

Expert verified
The elements in the set are 1, 2, 3, 4, 5, 6, 7, and 8.

Step by step solution

01

Identify Natural Numbers

Natural numbers are the positive integers starting from 1. Examples include 1, 2, 3, 4, etc.
02

Determine the Range

Find all natural numbers less than 9. This means identifying natural numbers from 1 up to, but not including, 9.
03

List the Elements

Write out the natural numbers that are less than 9: 1, 2, 3, 4, 5, 6, 7, 8.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sets
A set is a collection of distinct objects or elements. The elements in a set can be anything: numbers, letters, symbols, or even other sets. Sets are usually denoted with curly braces \( \{ \} \), and elements within a set are separated by commas. For example:

  • \(\{1, 2, 3\}\)
  • \(\{a, b, c\}\)
In the given exercise, we need to use these principles to list all elements that are natural numbers less than 9. This confined range simplifies our set to only include specific positive integers.
Positive Integers
Positive integers are whole numbers greater than zero. These include numbers like 1, 2, 3, 4, and so on. Another name for positive integers is 'natural numbers'. In the context of the problem, we are asked to identify natural numbers up to a particular limit (in this case, less than 9).

So, if we start from 1 and count upwards to the number just before 9, we form a sequence of positive integers: 1, 2, 3, 4, 5, 6, 7, and 8. These numbers are what make up our set of natural numbers less than 9.
Range in Mathematics
Range in mathematics often refers to the interval between a set of values or the difference between the highest and lowest values in a set. Here, we are dealing with the range of natural numbers starting from 1 and less than 9. The term 'less than 9' is critical because it indicates an upper boundary that is not inclusive.

The systematic range of our integers begins from 1 (the smallest natural number) and extends up to 8, since 9 is not included. By clearly defining both the starting point and the upper boundary, we ensure the completeness of our set: \(\{1, 2, 3, 4, 5, 6, 7, 8\}\).

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