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Chapter 1: Problem 22

Give three numbers between -6 and 6 that satisfy each given condition. Real numbers but not positive numbers

Short Answer

Expert verified
-6, -3, 0

Step by step solution

01

Understanding the Range

Identify the range of numbers between -6 and 6. This range includes all integers and real numbers from -6 to 6, inclusive.
02

Identifying Real Numbers

Since the numbers must be real, any number within the range of -6 to 6 can be considered as long as it is not complex or imaginary.
03

Selecting Non-Positive Numbers

Choose numbers within the range that are not positive. This means the numbers must be zero or negative.
04

Choosing Specific Numbers

Select three numbers from -6 to 6 that are either zero or negative. For example, -6, -3, and 0 are within the range and satisfy the given conditions.

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Key Concepts

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

Range of Numbers
The range of numbers between -6 and 6 includes all values from -6 up to and including 6. This range is continuous, meaning it incorporates all real numbers between these two endpoints.
To be specific, the range includes:
  • All integers like -6, -5, ..., 0, 1, 2, ..., 6
  • All fractions and decimal numbers within the interval, like -5.5, 3.14, 0.001, etc.
In mathematics, the notation for this inclusive range is \([-6, 6]\).
This helps us know the specific boundaries we're working with when selecting our numbers.
Non-Positive Numbers
Non-positive numbers are numbers that are either zero or negative. These numbers do not have a positive value and fall to the left of zero on the number line.
Here are the core points:
  • Non-positive numbers include all negative numbers and the number zero.
  • Zero (0) is a special case because it is neither negative nor positive but is included in the set of non-positive numbers.
  • Examples of non-positive numbers are: -3, -1, and 0.
In our exercise, we need to ensure any selected numbers meet this criterion, so we'll select from -6, -5, ..., 0.
Negative Numbers
Negative numbers are values that are less than zero. They have a negative sign (-) in front of them and are located to the left of 0 on a number line.
Key features of negative numbers include:
  • They are always less than zero (e.g., -1, -2.5, -100).
  • They represent a deficit or a position opposite to positive on a number scale.
  • In real-life contexts, they can describe things like loss, temperatures below freezing, and depths below sea level.
For our selection, we include any real number that falls within -6 and 0 as non-positive and negative.
Examples from our range could be -6, -3, and -1.

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