Is it true that every integer is a rational number?

Yes, it is true that every integer is a rational number. To understand why, let’s break down the definitions.

A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This means that a rational number can be written in the form:

r = a/b

where a and b are integers, and b cannot be zero.

Now, consider an integer. An integer is any whole number that can be positive, negative, or zero (for example, -3, 0, 5, etc.). Each of these integers can be written as a fraction. For instance:

• The integer 5 can be expressed as 5/1.
• The integer -3 can be expressed as -3/1.
• The integer 0 can be expressed as 0/1.

Since all integers can be written in the form of a fraction, they all satisfy the definition of rational numbers.

In conclusion, it is indeed true that every integer is a rational number, as every integer can be expressed as a fraction where the denominator is one, making it a subtype of rational numbers.