Explain what the vertical line test is and how it is used.
1 answer:
You might be interested in
Answer:
it is true
Step-by-step explanation:
We can demonstrate this by contradiction.
First choosing a random rational and assuming that exist two ways to represent this rational. Call that rational x, a, b and a', b ' the couples of relatively prime to express x.
Then we have
Isolating a:
a is an integer and a' is a relatively prime with b', for this reason b has to be a factor of b'. Suppose this factorization b'=nb, replacing it:
But now we have that n is a factor of a and is a factor of b, it means that a and b are not relatively prime, that is a contradiction with our premises. The sentence is true.
And referring to the positive denominator. If we want to express a positive rational the denominator and numerator will be both positive and if is a negative one we choose a positive denominator and a negative numerator.