Linear Algebra: Induction

Beginner course. Describes types of logic, and dives into proofs by induction.

5 flashcards · Mathematics · by lakesare

1. Explain 3 types of logical reasoning: deductive reasoning inductive reasoning abductive reasoning

   deductive reasoning - from premises to conclusion inductive reasoning - if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. abductive reasoning - equivalent to the logical fallacy of affirming the consequent. For all x, if x has pneumonia, then x has a fever. Doctor sees that someone has a fever, and conclu…

2. Mathematical Induction: how to prove that for all integers n ≥ a, P(n)?

   P(a) is true. For all integers k ≥ a, if P(k) is true then P(k + 1) is true. P(k) is called 'inductive hypothesis'

3. Use mathematical induction to prove that:

   We must prove that: P(1) is true. 2. For all integers k ≥ 1, if P(k) is true then P(k + 1) is also true.

4. Prove by induction the formula for a sum of a geometric sequence:

   1. Show that P(0) is true. 2. Show that P(k) → P(k+1).

5. Use mathematical induction to prove that:

   1. Show that P(0) is true. 2. Show that P(k) → P(k+1).