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Chapter 0: Problem 143

If you are given two real numbers, explain how to determine which is the lesser.

Short Answer

Expert verified
To determine which of two real numbers is lesser, compare them. If one number is positive and the other is negative, the negative number is less. If both numbers are positive, the number with the smaller absolute value is less. If both numbers are negative, the number with the larger absolute value is less. Before comparing, numbers may need to be converted to an equivalent form, such as decimals.

Step by step solution

01

Understand the values

First, it's essential to understand the given real numbers. Real numbers include both rational numbers (like 7, 0.6, and -15/3) and irrational numbers (like \(\sqrt{2}\), \(\pi\) and \(e\)). The question involves comparing these numbers to tell which is lesser.
02

Compare the Numbers

Once you're clear on the values of the numbers in question, compare them directly. This could mean simply looking at them (for instance, it's clear that 2 is less than 5), or it may involve some computation if the numbers are complicated (for instance, to compare \(\frac{1}{2}\) and \(\frac{2}{3}\), you could calculate their decimal equivalents and compare those). If the number on the left side is larger than the one on the right, the latter is the lesser number. Similarly, if the number on the right is larger, then the former is the lesser number.
03

Note the signs

Make sure to take into account the signs of the numbers. If one number is positive and the other is negative, the negative number is always less. Remember, any negative number is less than any positive number.

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