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Can you make an operator that takes any given irrational number and maps it onto the rationals?
Wiki User
∙ 11y ago
Of course not.
Number if Irrational Numbers is larger than number of rational numbers.
To be more exact: There is no one-to-one mapping of set of rational numbers
to the set of irrational numbers. If there would be such a mapping, their cardinality
(see Cardinality ) would be same.
In reality, rational numbers are countable (cardinality alef0)
real numbers, as well as irrational numbers are not countable (cardinality alef1).
These are topics in
wikipedia.org/wiki/Transfinite_number
theory
Wiki User
∙ 11y ago
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How do you find an irrational number between two irrational numbers?
There may be many easier and better ways, but here's how I would do it: -- Square the first given irrational number. -- Square the second irrational number. -- Pick a nice ugly complicated decimal between the two squares. -- Take the square root of the number you picked. It's definitely between the two given numbers, and it would be a miracle if it's not irrational.
Is the change in the value of an account when given to the nearest dollar a irrational number?
No, it is rational.
How do you define whether a given number is rational or irrational?
A rational number can be expressed as a simple fraction, an irrational number cannot. More formally: A rational number is any real number that can be expressed as a ratio of two integers (positive or negative whole numbers). (The denominator in the ratio cannot be zero.) An irrational number cannot be expressed in that way. The terms "rational" and "irrational" refer to the idea of "ratio".
How do you graph two integers the irrational number would fall between?
The answer will depend on the form in which the irrational number is given. For example, we know that pi is approx 3.14159 and so it falls between 3 and 4.
Which number is a irrational 317 25 0.6 33?
The given four numbers are all rational numbers
What irrational numbers can turn into a rational number?
No irrational number can turn into a rational number by itself: you have to do something to it. If you multiply any irrational number by 0, the answer is 0, which is rational. So, given the correct procedure, every irrational number can be turned into a rational number.
What is the irrational number closets to 13?
There is no such number. Irrational numbers are infinitely dense. Given any number near 13, there are more irrational numbers between that number and 13 than there are rational numbers in all.
How do you find an irrational number between two irrational numbers?
There may be many easier and better ways, but here's how I would do it: -- Square the first given irrational number. -- Square the second irrational number. -- Pick a nice ugly complicated decimal between the two squares. -- Take the square root of the number you picked. It's definitely between the two given numbers, and it would be a miracle if it's not irrational.
When can you say that a given real number is irrational?
A real number is an irrational number if it cannot be expressed as a fraction a/b, where a and b are integers. Most real numbers are irrational. The most well known irrational numbers are π and √2. The inverse condition are called the rational numbers.
Is the change in the value of an account when given to the nearest dollar a irrational number?
No, it is rational.
How can you prove that 3 plus 2x⁵ is an irrational number where x⁵ is irrational?
1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
How do you define whether a given number is rational or irrational?
A rational number can be expressed as a simple fraction, an irrational number cannot. More formally: A rational number is any real number that can be expressed as a ratio of two integers (positive or negative whole numbers). (The denominator in the ratio cannot be zero.) An irrational number cannot be expressed in that way. The terms "rational" and "irrational" refer to the idea of "ratio".
How do you graph two integers the irrational number would fall between?
The answer will depend on the form in which the irrational number is given. For example, we know that pi is approx 3.14159 and so it falls between 3 and 4.
Which number is a irrational 317 25 0.6 33?
The given four numbers are all rational numbers
Does circumference to diameter ratios have a pattern?
Yes. It is always {pi} ~= 3.14159265... It is an irrational number {pi} is actually more than just an ordinary irrational number; it is a transcendental number. Only the first 8 decimal digits are given above.
Are there fewer rational numbers than irrational numbers?
For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.
Can you add two irrational numbers to get a rational number?
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
