This is a blog for my second semester pre-calculus 30s students. Have a blast!

Thursday, May 04, 2006

Today's post

MAY 4, 2006

COUNTER EXAMPLES

Today's lesson is COUNTER EXAMPLES. It is about proving the CONJECTURE (conjecture: statement made by examples) wrong by providing true statements, examples, diagrams, equations. This lesson is somehow easy because all you do is prove that the conjecture is wrong. However, such conjectures may lead to sudden confusion because sometimes it gives just a small possibility of proving it wrong. You REALLY have to think about it too.
Here are some examples:
1) The sum of 2 prime numbers is always even. (CONJECTURE)
examples that verify this conjecture:
3 + 5 = 8 even
7 + 9 = 16 even
11 + 13 = 24 even
examples that contradict this conjecture:
7 + 2 = 9 odd
11 + 2 = 13 odd
13 + 2 = 15 odd
2) The expression 1 / x will always be less than 1 for any value of x.
examples that verify the conjecture:
x = 2
1 / 2 = 0.5
x = 4
1 / 4 = 0.25
examples that contradict the conjecture:
x = 1
1 / 1 = 1
x = 0.5
1 / 0.5 = 2
That's today's lesson. The homework is Exercise 48.
MAY 2, 2006

VENN DIAGRAMS

LESSON LAST TUESDAY:

EXAMPLES

A upside down U B = m, u

( B \ A ) ' = o, p, s, m, u, r


A \ B = o, p, s


( A U B ) ' = r

3 Comments:

Blogger John D. - #12 said...

Wow, Vince. Just wow. You rocked my socks off. That post was so cool.

5:48 PM

 
Blogger Mr. Malandrakis said...

Vince, this is an absolutely amazing post. Fantastic job to set an example.

10:53 AM

 
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