No.
5 and 2 are real numbers. Their difference, 3, is a rational number.
No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number
yes
The difference is that rational numbers stay with the same numbers. Like the decimal 1.247247247247... While an irrational number is continuous but does not keep the same numbers. Like the decimal 1.123456789...
The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...
No, it is always irrational.
It is always an irrational number.
No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number
They are not. Sometimes they are irrational. Irrational numbers cannot be expressed as a fraction.
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
Whole numbers can never be irrational.
The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.
Real numbers can be rational or irrational because they both form the number line.
Whole numbers are always rational.
All numbers are real. A number being irrational just means that is does not have a definite end.
There is no number which can be rational and irrational so there is no point in asking "how".
Yes. Google Cauchy's proof.