The Null Set
Image courtesy: Thomas Guignard
Okay, break's over. Time to get back to some Mad-Cool-Math Nuggets. Today we're going to delve into the wonderful world of set theory and achieve instant literary success in the process. Ready?
To define a mathematical set, think of all the books in your house. Each book is an element in the collection, or set, known as your library. We'll call this set L. Pick out your favorites and you have a subset of your library we could call F. Pick out the ones you've read more than once and make another subset called R (for repeat).
It's possible F = R, meaning every favorite has been read more than once and every book read more than once is a favorite.
Maybe your particular R is empty, meaning you never read a book more than once. In that case R would be an example of a null set, denoted {}. Another name for this is the empty set.
(If you hate to read and have no books then, like the image above, your L = {}. That, in my opinion, would be a sad null set indeed.)
Null sets, or sets that contain no elements, can be a little weird. They are a subset of every set you can think of, which means they must be a subset of themselves.
Say what? Let's go back to your library, the set L, whether it's empty or not. Consider the books written by my cat as a set called C. I love my cat, but she hasn't written any books. She doesn't even stand on my keyboard to type lsdkghkdjgsl. She's too busy sleeping in my bed all day. So the set C is empty or C = {}.
For C to be a subset of L, every book in C must be in L. Conversely, if C is not a subset of L, then there must be some book in C that is not in L. That's impossible, because C is empty and has no books. So C is a subset of L. (That, my friends, was a proof by contradiction. We mathy folk are tricksy, no?)
Have I blown your mind or bored you to sleep? I do apologize, but I did promise literary success, so let's get to it. Since a null set is a subset of every set, then I can say, without lying, that the set of my published novels is a subset of the books on the New York Times Bestseller List. I can also say that my published novels make a subset of the books that won the Pulitzer. How? Because the set of novels that I have published is a null set. Ta da!
Care to share something about your library set L? Is your subset of digital books bigger or smaller than your subset of paper books?
______________
Want to read something with no math involved, including a price? Feel "free" to download my sci-fi short short, The President and the Pea. The only confusing part is the unreliable narrator. Did Annette Hutchins really witness the assassination of the President of the United States? Or is she mental?
You explained that so well! I'm not a mathy, but I thought that was pretty cool. I feel smart! ;P
ReplyDeleteYeah! I'm glad you liked it.
DeleteThat was really interesting! No books would be sad, indeed.
ReplyDeleteThat is a cool math lesson, but reminds me of the novel I never finished.
ReplyDeleteMy mind is pretty much blown. Excuse me while I clean up the mess. :)
ReplyDeleteErmmm...let me read that again! ............ No, still a bit lost, but 'sums--and-things' was my worst subject at school!
ReplyDeleteIt’s officially the second half of A to Z. Time to catch that second wind, rest up on Sunday, then it’s that mad dash toward the finish line!
ReplyDeleteStephen Tremp
A to Z Cohost
N is for Numerology
Mind most definitely blown.
ReplyDeleteMaths scares me ;)
ReplyDeleteBut yes, my digital library is now far larger than my paper book collection. It's probably a good thing, though, because I was running out of bookshelves.
I admire your ability to understand and explain this logic. I got some of it, kind of.
ReplyDeleteWe gave away most all of our books, hard cover and paper back. I have gotten really lazy. I prefer to listen to someone read a book to me.
The disadvantage to have an audible version is that I like to see favorite phrases or passages written on the page. For that reason I have actually bought the hard copies of the last three books I have listened to.
I love null sets (and hate when I'm trying to solve matrices), but they can be fun. Among my stunning null sets is a subset of cars built by me that are simultaneously Nascar winners and Formula One champions.
ReplyDeleteRock on with your car-building self! ;)
DeleteI definitely need a math refresher course. I'm actually not saving as many books any more. I don't read them a second time so share them with other by donating them.
ReplyDeleteGreat idea. I need to clean out my shelves too.
Deleteadidas zx shoeshugged cheap neck, and suddenly adidas zx shoes felt so comfortable above all frightened suddenly gone. sale shouted climbed on my back, adidas factory outlet grabbed my neck. cheap tightly closed eyes, adidas zx shoes Seize the seat with one cheap adidas originals hand corner, the other hand slammed hard wrist grab cheap, cheap already adidas zx shoes lying on his back.
ReplyDelete20150708 junda
ReplyDeletemichael kors outlet
ed hardy clothing uk
mcm backpack
soccer outlet
burberry outlet
gucci handbags
oakley sunglasses sale
longchamp outlet online
gucci borse
air jordan uk
chanel bags
louboutin
gucci uk
oakley sunglasses
chanel handbags
oakley sunglasses outlet
nike blazer high
replica watches rolex
chaussure louboutin pas cher
coach outlet
kate spade new york
coach outlet store online
chanel outlet
coach outlet store online
oakley store
ralph lauren pas cher
oakley sunglasses cheap
ray bans
michael kors handbags
burberry handbags
prada outlet
pandora jewelry sale
jordan femme
michael kors uk
mont blanc pens
michael kors bags
air force pas cher
rolex watches for sale
cheap air max
10guowenhao0907
ReplyDeletesupra shoes
true religion outlet, http://www.truereligionjeansoutlet.com
lebron james shoes
michael kors outlet, http://www.michaelkorsoutlet-store.us.com
swarovski jewelry
dallas cowboys jersey
louis vuitton
air max 90
cheap soccer jerseys
ugg boots clearance,ugg australia,uggs on sale,ugg slippers,uggs boots,uggs outlet,ugg boots,ugg,uggs
replica handbags, http://www.replicahandbag.us.com/
marc jacobs
denver broncos jerseys
new balance shoes
ed hardy t-shirts
kobe bryants shoes
bottega veneta outlet
ray ban sunglasses
michael kors outlet online
coach outlet
hollister clothing
hollister canada, http://www.hollistercanada.com
louis vuitton outlet store, http://www.louisvuittonoutletstore.name/
pandora jewelry
michael kors outlet online, http://www.michaelkors-outlets.us.com
nba jerseys, http://www.nbajerseys.us.com
air jordan 13
kobe 9
mont blanc
oakley sunglasses, http://www.oakleysunglasses-wholesale.us.com/
louis vuitton uk
michael kors outlet
ray-ban sunglasses, http://www.ray-bansunglassess.in.net
louis vuitton handbags
cheap oakley sunglasses
chanel tote bag
ReplyDeleteburberry sale
chanel outlet
gucci luggage
louis vuitton travel bag
burberry shoes
burberry outlet
coach bags
gucci diaper bag
burberry crossbody bag
chanel diaper bag
michael kors bags on sale
coach purses
burberry store
coach hobo bag
mcm purses
coach outlet online
burberry bags
burberry handbag
cheap louis vuitton purses
michael kors handbags outlet
louis vuitton purses
louis vuitton eva clutch
cheap michael kors purses
prada-crossbody
prada handbags
coach factory outlet online
burberry bags
cheap michael kors handbags
gucci bag
michael kors crossbody
coach sunglasses
michael kors tote bags
coach crossbody bags
Quickbooks Support Phone Number
ReplyDeleteQuickbooks Enterprise Support Phone Number
Quickbooks Enterprise Tech Support Number
Quickbooks Enterprise Support Number
Quickbooks Enterprise Technical Support Number
Quickbooks Enterprise Tech Support Phone Number
Quickbooks Enterprise Technical Support Phone Number
Quickbooks Enterprise Help Desk Phone Number
Quickbooks Enterprise Help Desk Number
Quickbooks Enterprise Customer Service Number
Quickbooks Enterprise Customer Service Phone Number
Quickbooks Enterprise Customer Support Number
Quickbooks Enterprise Customer Support Phone Number
Aol Technical Support Phone Number
ReplyDeleteAol Technical Support Number
Aol Tech Support Number
Aol Tech Support phone Number
Aol Support Number
Aol Support phone Number
Outlook Technical Support Phone Number
Outlook Technical Support Number
Outlook Tech Support Number
Outlook Tech Support Phone Number
Outlook Support Number
Outlook Support Phone Number
Quicken Support Phone Number
ReplyDeleteQuicken Support Phone Number
Quicken Support Number
Quicken Tech Support Number
Quicken Tech Support Phone Number
Quicken Technical Support Number
Quicken Technical Support Phone Number
Quicken Technical Support Number
Quicken Tech Support Phone Number
Quicken Tech Support Number
sage support Number
ReplyDeletesage Support phone Number
sage Tech Support Number
sage Tech Support phone Number
sage customer service Number
sage customer service phone Number
sage Technical Support phone Number
sage Technical Support Number
sage Customer Support Number
sage Customer Support Phone Number
Quikcbooks Help
ReplyDeleteQuikcbooks Help
Quikcbooks Support Number
Quikcbooks Support Phone Number
Quikcbooks Tech Support Number
Quikcbooks Technical Support Number
Quikcbooks Tech Support Phone Number
Quikcbooks Technical Support Phone Number
Quikcbooks Helpdesk Phone Number
Quikcbooks Customer Service Phone Number
Quikcbooks Customer Service Number
Quikcbooks Customer Support Number
Quicken Help
Quicken Help
Quicken Support Number
Quicken Support Phone Number
Quicken Tech Support Number
Quicken Technical Support Number
Quicken Tech Support Phone Number
Quicken Technical Support Phone Number
Quicken Helpdesk Phone Number
Quicken Customer Service Phone Number
Quicken Customer Service Number
Quicken Customer Support Number
Sage Help
Sage Help
Sage Support Number
Sage Support Phone Number
SageTech Support Number
Sage Technical Support Number
Sage Tech Support Phone Number
Sage Technical Support Phone Number
Sage Helpdesk Phone Number
Sage Customer Service Phone Number
Sage Customer Service Number
Sage Customer Support Number
Quickbooks Technical Support Phone Number
ReplyDeleteQuickbooks Help
Quickbooks Support Phone Number
Quickbooks Tech Support Number
Quickbooks Tech Support Phone Number
Quickbooks Customer Support Phone Number
Quickbooks Customer Service Number
Quickbooks Customer Service Phone Number
Quicken Technical Support Phone Number
Quicken Help
Quicken Support
Quicken Tech Support Number
Quicken Tech Support Phone Number
Quicken Technical Support Phone Number
Quicken Customer Support Number
Quicken Customer Support Phone Number
Quicken Customer Service Number
Quicken Customer Service Phone Number
Sage Technical Support Phone Number
Sage Help
Sage Support
Sage Support Number
Sage Support Phone Number
Sage Tech Support Number
Sage Technical Support Number
Sage Technical Support Phone Number
Sage Customer Support Phone Number
Sage Customer Service Number
Quickbooks Technical Support Phone Number
Quickbooks Help
Quickbooks Support
Quickbooks Support Number
Quickbooks Support Phone Number
Quickbooks Tech Support Number
Quickbooks Tech Support Phone Number
Quickbooks Technical Support Number
Quickbooks Technical Support Phone Number
Quickbooks Customer Support Number
ReplyDeleteشركة تسليك مجارى الكويت شركة تسليك مجارى بالكويت
سباك الكويت سباك بالكويت
شركة تنظيف الكويت شركة تنظيف بالكويت