FOR THE STUDENT OF MATHEMATICS
PROPERTIES LIST 1.
Assume that p is any real number, q is any real number, r is
any real number and t is
any real number.
PROPERTY ADDITION MULTIPLICATION
I. p+q is a real number II. pq is a real number.
III. p+q = q+p IV. pq = qp
V. p+(q+r) = (p+q)+r VI. p(qr) = (pq)r
VII. p+0 = p = 0+p VIII. p1 = p = 1p
INVERSE (0 is not equal to 1):
IX. p+(-p) = 0 X. p(1/p) = 1 for p not = 0
XI. p(q+r) = pq+pr
Definition 1. Subtraction: p - q = p + (-q). Definition 2. Division for q not = 0, p/q = p (1/q)
PROPERTY EQUALITY p = q INEQUALITY p is less than q means p + t = q for positive t.
p = p XIII. p is not less than p
If p = q then q = p XV. If p is less than q, then q is not less than p.
TRANSITIVE: XVI. If p = q and q = r then p = r XVII. If p is less than q and q is less than r, then p is less than r.
SUBSTITUTION: XVIII. Any number, letter or algebra combination of numbers or letters
substituted for p, q, or r in the properties listed above unless stated otherwise.
Substitution: If a = b, then b may be put in place of a in any statement.
2 QUANTITIES = THE SAME:
XIX. If p = q and r = q, then p = r.
XX. If p = q, then p + r = q + r.
XXI. If p = q, then p r = q r.
XXII. If p = q, then p - r = q - r.
XXIII. If p = q, then p/r = q/r. r not equal to 0.
XXIV. If p = q and r = t, then p + r = q + t.
XXV. If p = q and r = t, then p/r = q/t. r , t not 0.
INVERSES FOR p:
XXVI. p's additive inverse is unique.
XXVII. p's multiplicative inverse is unique.
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