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They are only an infinitesimally tiny part of the set of real numbers.
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Why are numbers not rational?
Most numbers ARE rational. For instance all the integers and most real numbers are rational numbers. To be an irrational number a real number must be impossible to express as a ratio of integers.
Are rational numbers always integers?
Most of the time yes, positive or negative whole numbers count as rational numbers. So do positive or negative fractions.
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
Can negatives be rational?
Yes, negative numbers can most certainly be rational. A rational number is simply a number which can be expressed as a fraction. An example of a negative rational number is: -1/2
What is the history of rational numbers?
The history of rational numbers goes way back to the beginning of historical times. It is believed that knowledge of rational number precedes history but no evidence of this survives today. The earliest evidence is in the Ancient Egyptian document the Kahun Papyrus. Ancient Greeks also worked on rational numbers as a part of their number theory. Euclid's elements dates to around 300 BC. Indian mathematicians also worked on rational numbers. This is documented in different texts but the most important is probably the Sthananga Sutra which dates back to around the second century BC.
Why are numbers not rational?
Most numbers ARE rational. For instance all the integers and most real numbers are rational numbers. To be an irrational number a real number must be impossible to express as a ratio of integers.
Are positive numbers rational numbers?
Not necessarily. +sqrt(2) is positive but not rational.
Which set of numbers is the most reasonable to describe a person hat size?
rational numbers
Why do you use irrational nombers?
There are many common numbers in mathematics which are not rational. Two of the most important numbers in mathematics are pi and e: both are irrational.
Is the quotient of two nonzero numbers always a rational number?
Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.
Who invented rational numbers?
Well, no one knows who exactly 'invented' rational numbers. Most nations believed all numbers were rational until Pythagoreas proved this untrue by the square root of two.
Are rational numbers always integers?
Most of the time yes, positive or negative whole numbers count as rational numbers. So do positive or negative fractions.
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
What is the significance of irrational numbers with explanation?
A rational number is a number which can be expressed as a ratio of two integers. However, there are far more numbers that cannot be expressed in this fashion.The set of rational numbers is not closed under the basic operation of taking square roots. There are also other operations whose results are not rational numbers. The two most important constant of mathematics are pi (geometry) and e (calculus) and both are irrational numbers.
Can all whole numbers be rational?
yes, every whole number is rational since it can be written as a ratio. For example, the number 3 is really 3/1 which is a rational number. We define rational numbers as those numbers that we are able to write as ratios. However, most rational numbers are not whole numbersYes
What is the rational number?
There are infinitely many rational numbers and, in decimal form, most of them have infinitely many digits. So there cannot be a longest rational number.
Can negatives be rational?
Yes, negative numbers can most certainly be rational. A rational number is simply a number which can be expressed as a fraction. An example of a negative rational number is: -1/2
