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Chapter 1: Problem 60

Tell whether each statement is true or false. Every whole number is positive.

Short Answer

Expert verified
False; whole numbers include 0, which is not positive.

Step by step solution

01

Understanding Whole Numbers

Whole numbers are the set of numbers that include all natural numbers and zero. They start from 0, 1, 2, 3, and so on. It's crucial to remember that whole numbers can include 0.
02

Identifying Positive Numbers

Positive numbers are any numbers greater than zero. So 1, 2, 3, and so on are positive, but 0 is not considered positive because it is neither negative nor positive.
03

Evaluating the Statement

The statement claims that every whole number is positive. Since whole numbers include 0, which is not positive, the statement is false.

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Key Concepts

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

Positive Numbers
Positive numbers are numbers that have a value greater than zero. These numbers fall to the right of zero on the number line.
They are part of the set of whole numbers, but not all whole numbers are positive. For example, numbers like 1, 2, and 100 are positive. Zero is a critical point because it is neither positive nor negative.
  • Positive numbers are greater than zero.
  • They do not include zero or negative numbers.
  • Positive numbers are used in various real-life contexts like distances, temperatures above zero, and bank balances that show credit.
When a problem asks if every whole number is positive, remember to consider that 0 is included in whole numbers but is not positive.
Natural Numbers
Natural numbers are a subset of whole numbers that begin from 1 and go upwards indefinitely like 1, 2, 3, and so on. These numbers are used often in basic counting in everyday scenarios.
Natural numbers exclude zero since counting typically starts at 1. They do not include negative numbers or fractions; they are always whole and positive.
  • Natural numbers start at 1.
  • They are infinite, as you can continue counting endlessly.
  • Used in real-world counting, for example, the number of apples in a basket or days in a week.
In mathematics, when we refer to 'natural numbers,' we're considering only positive integers without including zero.
Zero
Zero is a unique number in the realm of mathematics. It is neither positive nor negative and plays a fundamental role in the number system. As part of the set of whole numbers, zero serves as the starting point for measuring distances, temperatures, and more on a number line.
It's crucial to understand its neutrality to avoid confusion in problems like the one in the exercise.
  • Zero is a whole number.
  • It is not a part of natural or positive numbers.
  • Acts as a placeholder in our numbering system, crucial for understanding the concept of nothingness or an empty quantity.
Recognizing zero's unique properties is important, especially when analyzing statements about whole numbers and whether they are positive, as zero does not fall into that category.

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