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Level 157

Real Numbers & Axioms of Equality


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a+b=b+a
Commutative Property of Addition
ab=ba
Commutative Property of Multiplication
(a+b)+c=a+(b+c)
Associative Property of Addition
(AB)C = A(BC)
Associative Property of Multiplication
a+0=a
Identity Property of Addition
1a=a
Identity Property of Multiplication
a+(-a)=0
Inverse Property of Addition
a(1/a)=1
Inverse Property of Multiplication
ax0=0
Multiplicative Property of Zero
a(b+c)=ab+ac
Distributive Property
Closure Property of Addition
If a and b are real numbers, then the sum of a+b is a real number
Closure Property of Multiplication
If a and b are real numbers, then the product of "a" times b is a real number
a=a
Reflexive Property of Equality
Symmetric Property of Equality
For all real numbers x and y, if x = y, then y = x.
Transitive Property of Equality
For all real numbers x, y, and z , if x = y and y = z, then x = z.
Substitution Property of Equality
For all real numbers x and y, if x = y , then y can be substituted for x in any expression and vice versa.
Addition Property of Equality
For all real numbers x, y, and z, if x = y, then x + z = y + z.
Subtraction Property of Equality
For all real numbers x, y, and z, if x = y, then x - z = y - z.
Multiplication Property of Equality
For all real numbers x, y, and z, if x = y, then xz = yz.
Division Property of Equality
For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.