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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.
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Are all number between 1 and 2 rational numbers?
No, there are more irrational numbers between 1 and 2 than there are rational numbers.
Are all numbers between 1 and 2 rational numbers?
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!
How many rational numbers less than 0.001?
Infinitely many.
When you multiply two rational numbers will you always get a number that is smaller than the two factors?
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.
What is the smallest digit that's common in all subsets of the rational numbers?
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.
Numbers existing between two rational numbers?
There are more irrational numbers between any two rational numbers than there are rational numbers in total.
What is the number of rational numbers between square root 3 and square root 5?
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.
Are all number between 1 and 2 rational numbers?
No, there are more irrational numbers between 1 and 2 than there are rational numbers.
Are there more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
Are more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.
Are all numbers between 1 and 2 rational numbers?
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!
What are all the numbers that are rational and less than -5?
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.
Is it possible to add 2 rational numbers and get a sum that is less than both the numbers you added?
I think so. -4 and -5 are both rational numbers. Their sum is -9, which is less than both of them individually.
What rational number is greater than 7 but less than 8?
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.
How many rational numbers less than 0.001?
Infinitely many.
When you multiply two rational numbers will you always get a number that is smaller than the two factors?
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.
What are rational numbers less than 5?
-- 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.
