Yes. Real numbers are points along a continuous infinite number line with its midpoint at 0.
Yes
Yes it is, but not every real number is a rational number
No, 0 does not have a reciprocal, yet 0 is a real number.
It is the real number whose length represents the distance from the zero on the line to the point on the line.
Yes. It's 9. The square root of every positive real number is a real number.
A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1. In the special case where b=0, a+0i=a. Hence every real number is also a complex number. And in the special case where a=0, we call those numbers pure imaginary numbers. Note that 0=0+0i, therefore 0 is both a real number and a pure imaginary number. Do not confuse the complex numbers with the pure imaginary numbers. Every real number is a complex number and every pure imaginary number is a complex number also.
Yes it is, but not every real number is a rational number
Yes every irrational and rational number is a real number.
The standard properties of equality involving real numbers are:Reflexive property: For each real number a,a = aSymmetric property: For each real number a, for each real number b,if a = b, then b = aTransitive property: For each real number a, for each real number b, for each real number c,if a = b and b = c, then a = cThe operation of addition and multiplication are of particular importance. Also, the properties concerning these operations are important. They are:Closure property of addition: For every real number a, for every real number b,a + b is a real number.Closure property of multiplication: For every real number a, for every real number b,ab is a real number.Commutative property of addition:For every real number a, for every real number b,a + b = b + aCommutative property of multiplication:For every real number a, for every real number b,ab = baAssociative property of addition: For every real number a, for every real number b, for every real number c,(a + b) + c = a + (b + c)Associative property of multiplication: For every real number a, for every real number b, for every real number c,(ab)c = a(bc)Identity property of addition: For every real number a,a + 0 = 0 + a = aIdentity property of multiplication: For every real number a,a x 1 = 1 x a = aInverse property of addition: For every real number a, there is a real number -a such thata + -a = -a + a = 0Inverse property of multiplication: For every real number a, a ≠ 0, there is a real number a^-1 such thata x a^-1 = a^-1 x a = 1Distributive property: For every real number a, for every real number b, for every real number c,a(b + c) = ab + bcThe operation of subtraction and division are also important, but they are less important than addition and multiplication.Definitions for the operation of subtraction and division:For every real number a, for every real number b, for every real number c,a - b = c if and only if b + c = aFor every real number a, for every real number b, for every real number c,a ÷ b = c if and only if c is the unique real number such that bc = aThe definition of subtraction eliminates division by 0.For example, 2 ÷ 0 is undefined, also 0 ÷ 0 is undefined, but 0 ÷ 2 = 0It is possible to perform subtraction first converting a subtraction statement to an additionstatement:For every real number a, for every real number b,a - b = a + (-b)In similar way, every division statement can be converted to a multiplication statement:a ÷ b = a x b^-1.
YES. Every whole number is a real number too.
No. There are infinitely many real numbers for every natural number.
No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.
No. There are infinitely many real numbers for every natural number.
Yes. Every integer is a rational number. Every rational number is a real number. Every real number is a complex number. The complex numbers include all real numbers and all real numbers multiplied by the imaginary number i=sqrt(-1) and all the sums of these.
Every irrational number is a real number.
No, a real number could also be a rational number, an integer, a whole number, or a natural number. Irrational numbers fall into the same category of real numbers, but every real number is not an irrational number.
No
No. 3.6427 is real and rational, but not a counting number.