Yes, the set of fractions between 1 and 2 is infinite.
This is because you can always find another fraction between any two given fractions. Consider the following:
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Finding a Fraction Between Two Others: Given any two distinct fractions, a and b, where a < b, the average of the two, (a + b)/2, will always be a fraction between them.
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Example: Let's start with 1 and 2.
- A fraction between 1 and 2 is 1.5 (or 3/2).
- Now, a fraction between 1 and 1.5 is 1.25 (or 5/4).
- A fraction between 1.5 and 2 is 1.75 (or 7/4).
- This process can continue indefinitely.
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Density of Rational Numbers: The rational numbers (which include fractions) are "dense" in the real numbers. This means that between any two real numbers (including 1 and 2), there exists a rational number. Since this holds true no matter how close together the real numbers are, it implies an infinite number of rational numbers between 1 and 2.
Therefore, because you can always find another fraction between any two fractions between 1 and 2, there are an infinite number of fractions between 1 and 2.
