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With the exception of zero, which is neither positive nor negative, every real number is either plus or minus. With positive number, the + sign is often implied and therefore is not always written [example: 3 and +3 both mean positive three]
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Whats real numbers?
A real number is any number between minus and plus infinity, or it is not an imaginary number.
Why minus into minus is plus?
It is an axiom necessary for the real numbers to form a field.
What is the square root of - 0.50?
there is no real square root of a minus number (think about it, minus x minus = plus, plus x plus=plus, and you can't have a minus x plus if it's a square root). However, there is an imaginary root which is "1/2i", where "i" represents the square root of -1. This number doesn't actually "exist" as such, it is just a theory which makes doing maths easier. However if you're not familiar with the concept of "i", you're probably not meant to end up with a minus square root (anything below A level further maths you don't usually need "i") . Check your calculations again.
Is the square of negative 54 rational'?
No, nor is it a real number. The square root of minus 54 is equal to the square root of plus 45, times i.
Is every irrrational number a real number?
Yes every irrational and rational number is a real number.
Whats real numbers?
A real number is any number between minus and plus infinity, or it is not an imaginary number.
Why minus into minus is plus?
It is an axiom necessary for the real numbers to form a field.
What is the square root of - 0.50?
there is no real square root of a minus number (think about it, minus x minus = plus, plus x plus=plus, and you can't have a minus x plus if it's a square root). However, there is an imaginary root which is "1/2i", where "i" represents the square root of -1. This number doesn't actually "exist" as such, it is just a theory which makes doing maths easier. However if you're not familiar with the concept of "i", you're probably not meant to end up with a minus square root (anything below A level further maths you don't usually need "i") . Check your calculations again.
Is the square of negative 54 rational'?
No, nor is it a real number. The square root of minus 54 is equal to the square root of plus 45, times i.
Every rational number is a real number?
Yes it is, but not every real number is a rational number
Is every irrrational number a real number?
Yes every irrational and rational number is a real number.
Order properties of real numbers?
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.
Since pi is not real does that mean that 1 plus or minus pi isn't real also?
pi IS real. It's irrational, but not unreal.
Is every whole number a real number too?
YES. Every whole number is a real number too.
Is every real number a natural number?
No. There are infinitely many real numbers for every natural number.
Is every real number is rational?
No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.
Is every natural is real number?
No. There are infinitely many real numbers for every natural number.
