properties of real numbers

reflexive property

Any quality is equal to its self

a = a

symmetric property

if one quantity equals a second quantity, then the second quantity equals the first.

if, a = b, then b = a

transitive property 

if one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity.

if, a = b and b = c, then a = c

additive identity property

for any number (a) the sum of that number (a) and zero is that number (a)

a + 0 = 0 + a = a

additive inverse property

a real number and its opposite are additive inverses of each other

a + (-a) = 0

multiplicative identity property

for any real number (a) the product of that number (a) and 1 is that number (a)

a . 1 = a

1 . a = a

multiplicative property of zero

for any real number (a) the product of that number (a) and 0 is 0

a . 0 = 0

0 . a = 0

multiplicative inverse property

for every real number (a/b) there is exactly one number (b/a) and that equals a/b . b/a = 1

associative property 

the way you group three or more numbers when adding g or multiplying does not change their sum or product.

(a + b) + c = a + (b + c) and (ab)c = a(bc).

commutative property

the order you add or multiply numbers does not change their sum or product

a + b = b + a and a . b = b . a