If a and b are rational, then a + p(b-a) where p is any number between 0 and 1, is rational and lies between a and b. So pick any 3 values for p.
If a and b are not rational, then find rationals u and v such that
a < u < v < b and repeat as above.
Cantor proved that between any two real numbers there are an infinite number of rationals which ensures the existence of u and v.
No, there are more irrational numbers between 1 and 2 than there are rational numbers.
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!
Infinitely many.
No. A rational number is ANY number that can be represented as one integer over a second integer (which cannot be zero). There is no requirement that the top integer is less than the bottom integer (an improper fraction is still a rational number - all integers are rational numbers as they can be represented as an improper fraction with a 1 as the denominator). Only if both rational numbers are less than 1 will the result of multiplying them together be less than both of them. If one rational number is greater than 1 and the other less than 1, then the result of multiplying them together is greater than the number less than 1 and less than the number greater than 1. If both rational numbers are greater than 1, then the result of multiplying them together is greater than both of them.
There is no such number. The empty set is a subset of rational numbers and, by definition, it contains no numbers so nothing that can be common to any other subset.Alternatively, all rational numbers less than -1 and all rational numbers greater than 1 are subsets of rational numbers. There is no number common to them.
There are more irrational numbers between any two rational numbers than there are rational numbers in total.
Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.
No, there are more irrational numbers between 1 and 2 than there are rational numbers.
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.
Here, the given rational number is 5 and it is also a whole number. It can also be expressed in fraction form as 5/1. We can determine all the whole numbers less than 5 as a rational number. Hence, 1, 2, 3, and 4 are the rational numbers less than 5.
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!
I think so. -4 and -5 are both rational numbers. Their sum is -9, which is less than both of them individually.
There are an infinite number of rational numbers that are greater than 7 but less than 8. Any fraction between those two numbers is a rational number, such as: 7 1/8, 7 1/4, 7 1/3, 7 1/2, or even numbers such as 7 4/784 or 7 452/453.
Infinitely many.
No. A rational number is ANY number that can be represented as one integer over a second integer (which cannot be zero). There is no requirement that the top integer is less than the bottom integer (an improper fraction is still a rational number - all integers are rational numbers as they can be represented as an improper fraction with a 1 as the denominator). Only if both rational numbers are less than 1 will the result of multiplying them together be less than both of them. If one rational number is greater than 1 and the other less than 1, then the result of multiplying them together is greater than the number less than 1 and less than the number greater than 1. If both rational numbers are greater than 1, then the result of multiplying them together is greater than both of them.
-- Every whole number that's less than 5 is a rational number less than 5. -- Every terminating decimal that's less than 5, and some that don't terminate, is a rational number less than 5. -- Every number less than 5 that you can completely write with digits is a rational number less than 5.