Term
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Definition
(p+q)+r = p+(q+r)
(p · q) · r = p · (q · r) |
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Definition
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Term
| Principle of Substitution |
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Definition
| If p = q, then p can be replaced by q. |
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Term
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Definition
| Given p ε R and q ε R, then one of the following has to be true: p < q, p > q or p = q |
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Term
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Definition
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Term
| Properties of Absolute Values |
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Definition
| |p| ≥ 0, |p| = |-p|, |p-q| = |q-p|, |pq| = |p| · |q|, |p/q| = |p| / |q|, |p|2 = p2 |
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Term
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Definition
| {x : x = p / q; p ε N, q ε N and q ≠0} |
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Term
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Definition
| Given p ε R & q ε R, then the distance between p and q is |p - q| |
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Term
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Definition
| p ε R, |p| is the distance of p from 0. If p < 0, then |p| = -p. If p ≥ 0, then |p| = p |
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Term
| Show the order of operations in order of most important to least important |
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Definition
Grouping Symbols
Exponents
Multiplication and Division from left to right.
Addition and Subtraction from left to right. |
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Term
| Quotients and products of real numbers with 0 |
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Definition
| p ε R, p · 0 = 0, 0 / p = 0, p ≠0 |
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Term
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Definition
| p ε R & q ε R. p / q = p (1/q); q ≠ 0 |
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Term
| Subtraction of Real Numbers |
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Definition
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Term
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Definition
| Any one of the numbers that are being multiplied or divided in a product or quotient expression. |
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Term
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Definition
| Any one of the numbers being added or subtracted in a sum or difference expression. |
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Term
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Definition
| A sequence of symbols that represent a product, quotient, sum or difference operation |
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Term
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Definition
| {x : x is on the number line and x is not in Q} = I |
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Term
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Definition
Given p ε R, q ε R, and r ε R, then
p(q + r) = pq + pr |
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Term
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Definition
| {x : x is in the counting sequence 1,2,3,4,...} = N |
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Term
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Definition
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Term
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Definition
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Term
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Definition
Given p ε R
p x 1 = p = 1 x p
p + 0 = p = 0 + p |
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Term
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Definition
Given p ε R,
p (1/p) = 1 = (1/p)p
p + (-p) = 0 = (-p) + p |
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Term
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Definition
Given p ε R and q ε R,
p + q ε R and pq ε R |
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Term
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Definition
Given p ε R, q ε R, and r ε R
Reflexive: p = p
Symetric: If p = q, then q = p
Transitive: if p = q and q = r, then p = r |
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Term
| Name the properties of addition and multiplication of real numbers |
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Definition
Closure
Associative
Commutative
Distributive
Identity
Inverse |
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Term
| Transitive Properties Of Inequality |
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Definition
Given p ε R, q ε R, and r ε R
If p < q and q < r, then p < r.
If p > q and q > r, then p > r. |
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Term
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Definition
| A ∩ B = {x : x ε A and x ε B} |
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Term
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Definition
| A U B = {x : x ε A or x ε B } |
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