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There are an infinite number of rational numbers between -1 and +1.

Take for example: N / (N+1) for any positive integer N: 1/2, 2/3, 3/4, 4/5, 5/6, etc.

This is just between +1/2 and +1, and still doesn't cover all of them. Consider 1/N for any non-zero integer: 1/1, 1/2, 1/3, 1/4, 1/5, etc. 1/(-1)=-1, 1/(-2)=-1/2, -1/3,-1/4, etc. There are an infinite number of schemes that you can come up with where the magnitude (absolute value) of the denominator is greater than the magnitude of the numerator.

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Q: What are rational numbers between negative 1 and positive 1?
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