Algebra Properties 9-7-2011

Transitive - If a = b and b = c, then a = c
If two things are equal to a middle thing, they are equal to each other.
Substitute a for b into b = c.  This gives a = c.

Reflexive - A thing is equal to itself
a = a

Symmetric - You can write an equality in either order
if a = b then b = a




Identity elements -

0 is what you add to a number to get the identical number

1 is what you multiply by a number to get the identical number

To get from a number to the identity element for addition, add the opposite of the number
To get from a number to zero, add the negative of the number
To get from 7 to 0, add -7
7 + (-7) = 0

To get from a number to the identity element for multiplication, multiply by the reciprocal of the number
To get from a number to 1, multiply by the reciprocal of the number
To get from 7 to 1, multiply by 1/7
7 * (1/7) = 1