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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
When were irrational numbers founded?
Probably when people tried to find the length of the diagonal of a unit square [sqrt(2)].
How do you write 15 million numbers?
Boy, I hope that's 15 million in numbers, since I'm not about to write 15 million numbers.
15,000,000
How can you tell if a number is irrational?
Because it is not represented as a ratio of two integers, one over the other.
And given the decimal expansion of it, it does not terminate, nor does any sequence of digits repeat forever at the end.
What is the sign for an irrational number?
There is no specific sign. The set of irrationals can be written as R - Q.
How can you prove that the square root of three is an irrational number?
Because 3 is a prime number and as such its square root is irrational
Could monkeys really write Shakespeare?
No. It's a mental or mathematical exercise, designed to give you a concept of infinity. Assuming an unlimited number of monkeys pecking at a keyboard, some of them of them are bound to hit an "N". In fact, an infinite number of them will hit "N" since infinity divided by the number of keys on a keyboard, or any other number for that matter, is still infinity. Of those infinite number of monkeys, another infinite number will hit the letter "o" next, and so an infinite number of them will type "Now is the winter of our discontent", or all of Richard III or all of Shakespeare's works for that matter.
But could they really do it? Of course not, since there is in reality not an infinite number of monkeys.
When is irrational numbers used in modern life?
"Irrational" numbers are the name for numbers that cannot be expressed in fractions; that is, in a "ratio" of one number to another. The number .5 is 1/2; one divided by two.
The most useful "irrational" number is the number "pi", the ratio of the diameter of a circle divided by its circumference. There is no fraction that exactly equals "pi", although 22/7 is close.
Another irrational number is the number "e", the root of the "natural logarithms". This is extensively used in engineering and electronic calculations.
Is non terminating but repeating decimals are irrational numbers?
If there's a repeating sequence then it's a rational number.
No because 102 squared is 10404 which is a rational number
Is the set of irrational numbers closed under mulriplication?
No. You can well multiply two irrational numbers and get a result that is not an irrational number.
