where α is a real number, 0 < α≤ 1, is also a metric of the field R. In the definition of a metric, conditions (1) and (3) are clearly satisfied. Let |x|≥ |y|, x≠ 0. Then |x+y|α=|x|α|1+xy|α≤|x|α(1+|yx|)α≤|x|α(1+|yx|)≤|x|α(1+|yx|α)...
Simple fractions whose numerators and denominators are whole numbers are rational numbers. For example, the fraction 2/5 is a rational number. However, the fraction 1.3/5 is not a rational number since 1.3 is not an integer according to the definition of a rational number. ...
Incomputer science, it is significant if a number is rational or irrational. A rational number can be stored as an exact numeric value, while an irrational number must be estimated. NOTE:The number zero (0) is a rational number because it can be written as 0/1, which equals 0. ...
If n is an odd number, just use xn=n. This is a positive odd number, and thus xn∈O. Moreover, by the definition of f, we have that f(xn)=n. If n is an even number (so n≥2), we can write n=1+(n−1), with (n−1) being a positive odd integer number. Thus (...
√2 (square root of 2) ? NO !Oops! The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they are not rational they are called Irrational.Another famous irrational number is Pi (π):Formal Definition of Rational NumberMore...
Proof of an Irrational number:Let's understand how to prove that a given non-perfect square is irrational. Here is stepwise proof of the same.To prove: √2 is an irrational number.Suppose, √2 is a rational number. Then, by the definition of rational numbers, it can be written that,...
Consider a number {eq}\begin{align} \displaystyle \frac{3}{15}\\ \end{align} {/eq}, it is in the form of fraction so it is a rational number. Agai... Learn more about this topic: Rational vs. Irrational Numbers | Definition & Difference ...
Learn the definition of Rational and browse a collection of 616 enlightening community discussions around the topic.
A rational number. Rationale (law) an explanation of the fundamental reasons (especially an explanation of the working of some device in terms of laws of nature); The rationale for capital punishment The principles of internal-combustion engines Rational Capable of reasoning. Man is a rational cre...
Rational Numbers | Definition, Forms & Examples from Chapter 19 / Lesson 19 542K What is a rational number? Learn about rational numbers, rational numbers examples, irrational numbers, and their use in math. Also learn about ratios. Related to this Question Is 144 a rational number? Is...