## Math Theorems

##### Description:

here are the math theorems from the notes... i didn't get stephens so i made these.

##### Classes:

Cistercian Class of 2013

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# Math Theorems

 Addition Property of Equality (Thm 1)For all a, b, c, in R if a=b, then a+c=b+c
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#### Definitions

Addition Property of Equality (Thm 1) For all a, b, c, in R if a=b, then a+c=b+c
Cancellation Property of Addition (Thm 2) For all a, b, c, in R if a+c=b+c, then a=b
Opposites of Sums (Thm 3) For all a, b, in R, -(a+b)=(-a)+(-b)
Opposites of Opposites (Thm 4) For all a in R, -(-a)=a
The Multiplicative Property of Equality (Thm 5) For all a, b, c, in R if a=b then ac=bc
Cancellation Property of Multiplication (Thm 6) For all a, b, c, in R if ac=bc and c is not equal to 0, then a=b
Reciprocals of Products (Thm 7) For all a, b, in R where a,b are not equal to 0, 1/ab=(1/a) (1/b)
Reciprocals of Reciprocals (Thm 8) For all a in R where a is not equal to 0, a=1/1/a
Multiplicative Property of Zero (Thm 9) For all x in R x*0=0
Converse of the Multiplicative Property of Zero (Thm 10) For all a,b in R if ab=0, then a=0 or b=0
Multiplicative Property of (-1) (Thm 11) For all a in R (-1)a=-a
Multiplying by Opposites (Thm 12) For all a,b in R (-a)b=a(-b)=-(ab)
Subtracting the Opposite (Thm 13) For all a,b in R a-(-b)=a+b
Non-Commutative Property of Subtraction (Thm 14) For all a,b in R a-b= -(b-a)
Non-Associative Property of Subtraction (Thm 15) For all a,b,c in R a-(b-c)=(a-b)+c
Dividing by the Reciprocal (Thm 16) For all a,b in R where b is not equal to 0 a/1/b=a*b
Non-Commutative Law for Division (Thm 17) For all a,b in R where a,b are not equal to 0, 1/a/b=b/a
Non-Associative Law for Division (Thm 18) For all a,b,c in R where b,c are not equal to 0, a/(b/c)=ac/b
Multiplication of "Fractions" (Thm 19) For all a,b,c,d where b,d are not equal to 0, a/b*c/d=ac/bd
Division by "Fractions" (Thm 20) For all a,b,c,d in R where b,c,d are not equal to 0, a/b/c/d=ad/bc
The Transitivity of Inequality (Thm 21) If a<b and b<c, then a<c
The Addition Property of Inequality (Thm 22) For any real numbers a,b,c, if a<b, then a+c<b+c
The Multiplication Property of Inequality (Thm 23) A) If a<b and c>0 then ac<bc
B) If a<b and c<0 then ac>bc
The Inequality of the Opposite (Thm 24) If a>0, then -a<0
The Inequality of the reciprocal (Thm 25) If a>1 then 0<1/a<1
The Square is Never Negative (Thm 26) For all real numbers a, a²≥0
Inequalities Added (Thm 27) If a<b and c<d, then a+c<b+d

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