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Chapter 2: Problem 73

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The humor in the cartoon is based on the fact that "rational" and "real" have different meanings in mathematics and in everyday speech.

Short Answer

Expert verified
The statement makes sense. The humor of the cartoon is derived from the play on words, or pun, involving the different meanings of the terms 'rational' and 'real' in mathematics and everyday usage.

Step by step solution

01

Understanding Mathematical Terms

In mathematics, 'rational' refers to any number that can be expressed as a quotient or fraction p/q of two integers, with the denominator q not equal to zero. A 'real' number is a value of a continuous quantity that can represent a distance along a line, encompassing both rational and irrational numbers (those that can't be represented as a simple fraction).
02

Understanding Everyday Usage

In everyday speech, these words have different meanings. 'Rational' refers to thinking logically or reasonably, or behavior guided more by conscious thought than by emotions. 'Real' means existing or occurring in physical reality, not imagined or supposed.
03

Making the Comparison

The humor in the cartoon arises from the interplay between these different meanings. For example, a joke can be made on the idea that a 'rational' person, one who thinks logically, might not be 'real' or authentic in everyday circumstances, like a 'rational' number that doesn't exist in the 'real' number line (like square root of -1).

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