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Irrational Numbers
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.
3,962 Questions
How do you find the rational form of a negative fraction?
To write something in rational form means to write it as a fraction. If you are given a negative number in the form of a fraction, it is already in rational form.
If you are given a decimal and wish to turn it into a fraction, just use 10, 100, etc as the denominator. In the case of a repeating decimal there is a method but that's another question!
What computer was the first to calculate pi and to how many digits?
Pi was calculated, and could be written to any number of places you wanted
if you were willing to spend the time at it, hundreds of years before anbody
ever imagined the idea of a computer.
What numbers is binary made up of?
Binary has all the numbers.
Each binary digit can have the value 0 or 1 only.
There are countably infinite rational numbers. That is, it is possible to map each rational number to an integer so that the set has the same number of elements as all integers. This is the lowest order or infinity, Aleph-null.
The number of irrationals is a higher order of infinity: 2^(Aleph-null). This is denoted by C, for continuum.
There are no orders of infinity between Aleph-null and C.
How many irrational numbers are there between 1 and 5?
An infinite number, some of which will be k times pi where k is any fraction which brings the result into the required range. Others will be j times e similarly, or q x square-root of 2, and so on and so on.
How do you tell rational numbers?
If they are able to be expressed as a fraction.
For example: 1 = 1/1
0.5 = 1/2
Is -5 over 8 a real number or an integer or a rational number or an irrational number?
It is a real and rational number.
Can finite sets could be infinite sets?
The way I understand it, a finite set can not be an infinite set, because if it were
an infinite set, then it would not be a finite set, and the original premise would
be violated.
Which subsets of numbers cannot be irrational?
Integers, rationals. Also all subsets of these sets eg all even numbers, all integers divided by 3.
What is the value of a transcendental number?
All real transcendentals are irrational, and therefore their exact value cannot be determined. Some examples are pi and the natural logarithmic base (usually called 'e'); see the related questions for fairly accurate values of these.
The same cannot be said for all complex numbers, and since it is overly difficult to prove whether a number is transcendental, we have no examples of a transcendental complex number to give yet.
