FOR THE STUDENT OF MATHEMATICS
PROPERTIES LIST 3.
Starting with Property XIX on Properties List 1, challenge yourself to show how each property may result from earlier properties.
Assume that p is any real number, q is any real number, r is
any real number, t is
any real number and u is
any real number.
Definition 5. p4 = pppp
IL. ( p + q )4 = p4 + 4p3q + 6p2q2 + 4pq3+ q4
L. ( p + q ) ( r + t + u ) = ( p + q )r + ( p + q )t + ( p + q )u = pr + qr + pt + qt + pu + qu
LI. If pq = 0, then p = 0 or q = 0
NUMBERS AND GEOMETRY
The numbers p and q may locate points on one line so: p and q locate
the same point when p = q. p and q locate different points when
not equal to each other, p ≠ q .
Definition 6. Absolute Value is written | p - q | and is the positive one of ( p - q ) or ( q - p ).
If p and q locate points on a horizontal line then the absolute value of ( p - q ) gives the distance between p and q. | p - q | means the distance between p and q.
Definition 7. In geometry distance between p and q corresponds to the absolute value | p - q | in algebra.
List #1 Link
List #2 Link
List #4 Link
List #5 Link and
LII. | p | is a positive number or zero
LIII. | p q | = | p | | q |
LIV. | p/q | = | p |/| q |
LV. || p || = | p |
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