Sorry, I have not been posting for a while I have been going from doctor’s appointments to doctor’s appointments in all my free time (or blogging time). Therefore to makeup for my lack of posting I’m going to make this post really…really long and hopefully I will be able to cover everything we learned.

a) This weeks POW: kicks and hugs

In order for us to successfully complete this weeks POW our class decided to….

1) have the first person in line to count the number of “kicks” on everyone’s back

2) if there is an even amount of  “kicks” the first person says “hugs” , but if there is an odd number of “kicks” the first person says kicks

3) after that it is up to the people in line to keep track of how many said “kick” or “hug”

AND we all get 100% 🙂

b) Equivalent Relations

For there to be an equivalent relation between to sets it must pass all three of the conditions: reflectivity, symmetry, and transitively.

Lets talk about Harry Potter….

example: Let s={students at Hogwarts}. Define s(1)~s(2) <=> s(1), s(2) elements of the same house

1) reflexive: Must be able to wiggle its self. For every s element of S, s~s. For this example: Harry Potter wiggles Harry Potter (check!)

2) symmetry: If it wiggles one-way it must wiggle the other way as well. For every a,b element of s , a~b => b~a. For this example: Harry Potter wiggles Ron implies Ron wiggles Harry Potter, since Harry and Ron are both in Gryff. this statement holds true. (check!)

3) transitively: There must be a third element in the set that wiggles both previous elements. For all a,b,c element of S such that a~b and b~c =>a~c. For this example: Harry wiggles Ron and Ron wiggles Hermione, implies that  Harry wiggles Hermione (what a love triangle). This shows that the third element, Hermione, also belongs to the same house, Gryff. (check!)

Thus this is an example of an equivalent relation. But what is in it equivalent class??

c) Equivalent Classes

Denoted as s/~={equivalent classes)

From the example as before the equivalent classes is…

s/~={Gryff., Hufflepuff, Ravenclaw, Slytherin}

To represent an element in one of the classes use the symbol “[…]”. For example: [Neville] = [Harry Potter] element of s/~

d) Induction

STRONG  induction <=> (WEAK) induction

Mind blowing weak induction and strong induction are actually the same thing and can be used interchangeably. Similar to contradiction and a orginal proof, these to methods can be used for the same proofs. It seems odd because it is harder(or seems impossible) to prove some theories using one method, but by using the other method it becomes simple.

I didn’t really elaborate very much on induction because I already have last weeks post about it, so check that one out.

Thanks for reading, plus I do believe Casey told the 1:20 class to call out Brad for missing class and for ultimately missing a STRONG induction proof example.





Posted on April 7, 2013, in Uncategorized. Bookmark the permalink. Leave a comment.

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