L26_Wed_Mar_24

# L26_Wed_Mar_24 - MAE3811Sp 2010 Mahoney1 From Last time...

This preview shows pages 1–3. Sign up to view the full content.

1 MAE3811–Sp. 2010 Mahoney–1 From Last time…. Division In Depth Recall, it was recent, that for any integers a and b , with b not equal to 0 , a ÷ b = c if and only if c is the unique whole number such that b∙c = a . We say b divides a , written b | a , if, and only if, there is a unique integer q such that a = bq . If b | a , then b is a ______________ or a __________________ of a . a is a ___________________ of b . q usually stands for the ___________________ of a and b True or False (a - b) | a 2 –b 2 , a not equal to b 0 | 0 MAE3811–Sp. 2010 Mahoney–2 Properties of divisibility Recall a | b means…. Theorem: a | b if and only if a | -b Proof: Theorem: if d | a, and n is any integer, then d | na Proof:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 MAE3811–Sp. 2010 Mahoney–3 Properties of divisibility II Let a, b, and d be any integers with d ≠ 0. Theorem: If d | a and d | b, then d | (a + b). Proof: Corollary: d | a and d | b, then d | (a - b) Proof: MAE3811–Sp. 2010 Mahoney–4 Proof by Contradiction Proof by contradiction is a method of Proof often used when you wish to prove the
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 07/22/2011 for the course MAE 3811 taught by Professor Mahoney during the Spring '11 term at University of Florida.

### Page1 / 6

L26_Wed_Mar_24 - MAE3811Sp 2010 Mahoney1 From Last time...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online