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The Real numbers.

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โˆ™ 2013-12-28 18:32:40
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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: What is a set of numbers made up of rational and irrational numbers?
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What is made up of rational and irrational numbers?

The set of real numbers.


Why 2 set are irrational and rational are separate?

Because irrational numbers are defined as those that are not rational. The dichotomy means that every real number belongs to one or the other of these sets, and never to both.


Why is the sum of a rational numbers and an irrational number is irrational?

Let x be a rational number and y be an irrational number.Suppose their sum = z, is rational.That is x + y = zThen y = z - xThe set of rational number is closed under addition (and subtraction). Therefore, z - x is rational.Thus you have left hand side (irrational) = right hand side (rational) which is a contradiction.Therefore, by reducio ad absurdum, the supposition that z is rational is false, ie the sum of a rational and an irrational must be irrational.


What are the different types of numbers And where did they originate from?

From the simplest to more complicated, there are:N, the set of Natural or counting numbers [0], 1, 2, 3, ...Z, the set of all integers, ..., -3, -2, -1, 0, 1, 2, 3, ...Q, the set of all rational numbers (Q for quotient). These are numbers of the form p/q where p and q are integers and q is not 0.Irrational numbers, such as sqrt(2), e, cuberoot(171/2) and so on. These cannot be expressed in the form of a ratio and so are not rational.Transcendental numbers are a special type of irrational numbers. Most well known irrational numbers arise as solutions to [non-constant] polynomials with rational coefficients. However, there are numbers such as pi and e (extremely important to mathematics) which are transcendental.R, the set of Real numbers are made up of the rational and irratoinal numbers.C, the set of complex numbers. These have a part that is real (as above) and a part that is iaginary - related to the square root of -1.All these numbers originated in the human mind!


What number categories does -3.75?

Negative rational numbers; Negative real numbers; Rational numbers; Real numbers. The number also belongs to the set of complex numbers, quaternions and supersets.

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