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| Operations | |
|---|---|
| Name | Property |
| Distributive Property | a * (a+c) = a * b + a * c |
| Commutative Property of Addition | a + b = b + a |
| Commutative Property of Multiplication | a * b = b* a |
| Associative Property of Addition | (a+b)+c = a + (b+c) |
| Associative Property of Multiplication | (a* b)* c = a * (b * c) |
| Identities | |
|---|---|
| Name | Property |
| Additive Identity | a+0 = a |
| Multiplicative Identity | a*1=a |
| Equalities | |
|---|---|
| Name | Property |
| Addition Property of Equality | If a=b, then a+c=b+c |
| Subtraction Property of Equality | If a=b, then a-c=b-c |
| Multiplication Property of Equality | If a=b, then a* c=b* c |
| Division Property of Equality | If a=b, then a/c=b/c |
| Reflexive Property of Equality | Any real number is equal to itself |
| Symmetric Property of Equality | If a=b, then b=a |
| Transitive Property of Equality | If a=b and b=c, then a=c |
| Closure Property of Real Numbers | |
|---|---|
| ∀ a,b ∈ R ⇒ a + b ∈ R | Closed Under Addition |
| ∀ a,b ∈ R ⇒ a - b ∈ R | Closed Under Subtraction |
| ∀ a,b ∈ R ⇒ a * b ∈ R | Closed Under Multiplication |
| ∀ a,b ∈ R ⇒ a ÷ b /∈ R | Not Closed Under Division |