Math and Arithmetic

Algebra

# Does every real number have a reciprocal?

###### Wiki User

###### 2010-09-08 04:31:40

No, 0 does not have a reciprocal, yet 0 is a real number.

## Related Questions

###### Asked in Numbers

### What is the reciprocal of a real number?

The reciprocal of a number is one divided by the number. The
product of a number and its reciprocal equals one.
The easiest way to get the reciprocal of a number is to put the
number in the form of a fraction then swap the numerator with the
denominator.
The reciprocal of 2/3 is 3/2.
The reciprocal of 123/5564 is 5564/123.
The reciprocal of 1/5 is 5.
The reciprocal of 73 is 1/73.
The reciprocal of x is 1/x.

###### Asked in Math and Arithmetic

### What is the reciprocal of 10.1?

The reciprocal of any number is 1 divided by that number.
Therefore, the reciprocal of 10.1 is 1/10.1.
The reciprocal of any number is 1 divided by that number.
Therefore, the reciprocal of 10.1 is 1/10.1.
The reciprocal of any number is 1 divided by that number.
Therefore, the reciprocal of 10.1 is 1/10.1.
The reciprocal of any number is 1 divided by that number.
Therefore, the reciprocal of 10.1 is 1/10.1.

###### Asked in Math and Arithmetic, Algebra, Colleges and Universities

### Order properties of real numbers?

The standard properties of equality involving real
numbers are:
Reflexive property: For each real number a,
a = a
Symmetric property: For each real number a, for
each real number b,
if a = b, then b = a
Transitive property: For each real number a, for
each real number b, for each real number c,
if a = b and b = c, then a = c
The 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 + a
Commutative property of multiplication:
For every real number a, for every real number
b,
ab = ba
Associative 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 = a
Identity property of multiplication: For every
real number a,
a x 1 = 1 x a = a
Inverse property of addition: For every real number
a, there is a real number -a such that
a + -a = -a + a = 0
Inverse property of multiplication: For
every real number a, a ≠ 0, there is a real number
a^-1 such that
a x a^-1 = a^-1 x a = 1
Distributive property: For every real number a,
for every real number b, for every real number c,
a(b + c) = ab + bc
The 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 = a
For 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 = a
The definition of subtraction eliminates division by 0.
For example, 2 ÷ 0 is undefined, also 0 ÷ 0 is undefined, but 0
÷ 2 = 0
It is possible to perform subtraction first converting a
subtraction statement to an addition
statement:
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.