Problem 1 Use set notation to list the des... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 1

Use set notation to list the described elements. The hours on a clock.

Short Answer

Expert verified

The hours on a clock are $ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\} $.

Step by step solution

Understand the Problem

We need to represent the hours on a clock as a set. In standard clocks, there are 12 hours that repeat twice in a day (AM and PM), but we are only concerned with the numbers themselves.

Identify the Elements to Include

Identify what constitutes the 'hours' on a standard clock. These are the integer numbers from 1 to 12.

Write the Set in Set Notation

Use set notation to represent the set of hours. In set notation, we list the elements we wish to include. Thus, the set of hours on a clock is written as $ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\} $.

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Key Concepts

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

Clock Hours

The concept of clock hours is integral to understanding time and how we represent it in everyday life. A standard analog clock, which many of us use or are familiar with, displays the time using hour numbers from 1 to 12.

These numbers do not exceed 12, after which they cycle back to 1. For example, after 12 PM comes 1 PM, demonstrating the cyclical nature of clock hours.
This pattern repeats itself twice throughout a 24-hour period, once for AM and once for PM.
Understanding clock hours helps in scheduling and planning throughout the day, as activities are often associated with specific times, like 9 AM for starting school or work.

It's interesting to note that clocks are a practical application of modular arithmetic, known as "modular 12" for traditional clocks. This kind of understanding supports mathematical concepts, such as integers and sets, which we'll delve into next.

Integer Numbers

Integer numbers are whole numbers that can be positive, negative, or zero, and are fundamental to mathematics. When we discuss the hours on a clock, we specifically use integer numbers ranging from 1 to 12.

The numbers 1 through 12 are positive integers, reflecting the sequence of time as we read it on the clock.
Integer numbers do not include fractions or decimals, which means the clock does not display something like 3.5 as an hour.
This characteristic ensures clarity and simplicity in representing time in a standardized way without confusion.

In broader mathematics, integer numbers are denoted by the symbol $ \mathbb{Z} $, but when it comes to clocks and time, we deal with a finite, very specific subset of these integers, which brings us to the concept of set representation.

Set Representation

Set representation is a mathematical concept where a collection of distinct objects is grouped together. These objects can be anything, including numbers, and they collectively form a "set."

In the case of clock hours, the set is made up of integers representing each hour: $ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\} $.
Set notation helps in listing these elements in such a way that they are clear and concise, surrounded by curly braces $ \{\} $.
When using set representation for clock hours, it's important to note that each element is unique and there is no repetition, even though in practice, the cycle repeats after 12.

Set notation is particularly useful in mathematics and computing for defining collections that can be manipulated or examined for properties or patterns, mirroring how we organize time in discrete intervals on a clock.

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91影视

Use set notation to list the described elements. The hours on a clock.

Short Answer

Step by step solution

Understand the Problem

Identify the Elements to Include

Write the Set in Set Notation

Key Concepts

Clock Hours

Integer Numbers

Set Representation

One App. One Place for Learning.

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