No
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a ratio of integers
Then they are, simply, two different integers. Any two positive integers will do, according to the specification.Then they are, simply, two different integers. Any two positive integers will do, according to the specification.Then they are, simply, two different integers. Any two positive integers will do, according to the specification.Then they are, simply, two different integers. Any two positive integers will do, according to the specification.
- Always, if the two integers are both positive. - Sometimes, if the two integers have different signs. - Never, if the two integers are both negative.
Yes.Suppose a and b are two positive rational numbers. Then a can be expressed in the form p/q where p and q are positive integers, and b can be expressed in the form r/s where r and s are positive integers.Then b - a = r/s - p/q = (qr - ps)/qs.Now, since p, q, r and s are integers, thenby the closure of the set of integers under multiplications, qr, ps and qs are integers;q and s are positive => qs is positive, andby the closure of the set of integers under addition (and subtraction), qr - ps is an integer.That is, b - a = (qr - ps)/qs is a ratio of two integers, where the denominator of the ratio is positive.
A number that cannot be expressed as the ratio of two integers is known as an irrational number.