| Question | Answer |
| "In the direction" vectors | a ∈ Fn is in the direction of b ∈ Fn if there is a non negative real scalar k so that b = ka or a = kb |
| Parallel Vectors | a ∥ b, if there is a scalar k so that b = ka or a = kb |
| Components of a vector | The scalar quantities |
| Vector | An Ordered N-Tuple in F^n |
| Real Numbers | Bold Rational and Irrational Numbers |
| Absolute Value of a Complex Number | |z|= Square root of a^2 +b^2 |
| Imaginary Unit | The complex number i = (0, 1). Or, a + bi |
| Product of Complex Numbers | z = (a,b) and w = (c,d) is the complex number def zw = (ac−bd,ad+bc) |
| Set of Complex Numbers | C = { (a,b) : a, b ∈ R} |
| Complex Number | An ordered pair (a, b) of real numbers |
| Mathematical Induction vs. Inductive Reasoning | Despite its name, mathematical induction is not a form of inductive reasoning. Inductive reasoning attempts to draw general conclusions from specific facts. Mathematical induction is a form of deductive reasoning and is completely rigorous. |
| Principal of Complete Induction | Let P0, P1, P2, . . . be a sequence of statements. If (i) P0 is true, and (ii) for all natural numbers k, if Pj is true for all natural numbers j ≤ k, then Pk+1 is true, then Pn is true for every natural number n. |
| Integers | Natural numbers and their negatives ...-2,-1,0,1,2... Symbolized by Z or C |
| The Induction Step | Prove that for all natural numbers k, if Pk is true, then Pk+1 is true. |
| The Base Case | Prove that P0 is true. |
| Principal of Mathematical Induction | Let P0, P1, P2, . . . be a sequence of statements. If (i) P0 is true, and (ii) for all natural numbers k, if Pk is true, then Pk+1 is true, then Pn is true for every natural number n. |
| Natural Numbers | Non-negative counting numbers. 0,1,2,3... Symbolized by N |
17 cards - created sep 29, 8:28pm
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