Emptyset
You are welcome. However I feel that I should tell you that my major professor seriously doubted your existence on the the grounds that a set is a collection of things and, therefore, could not be empty.
Wednesday, April 13, 2011
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Questions from a non mathematician. In serious mathematics is a “set” considered an object in its own right or simply a name for a collection of things?
ReplyDeleteIs a six pack of XX an object or a name for a collection of things?
ReplyDeleteSomeone named "Empty Set" must surely know the answer.
Michael apparently knows the answer is yes, that a set is an object in it own right...in fact I think that Tom does too.
ReplyDeleteSuppose Jack, a consumer of beer, lives in the city X, Suppose as well that Jack brews for the residents of city X all the beer which the residents do not brew for themselves and only that beer which the residents do not brew for themselves. Does Jack brew beer for himself? In other words, is Jack a member of the set of all residents of the town for whom Jack brews beer?
Jack's story is obviously a sad one, yet leavened with hope and inspiration. He retired in X at the relentless urging of his wife after having succumbed to the relentless pressures of his profession as the head taster at the XX Beer Brewery, known as XXBB locally. His wife had always said it was because she wanted to be closer to her aging parents, but she confided to some of her friends that "Jack had a small, ... ahem, problem," one she thought that the fact that X County was dry might help. Her strategy proved remarkably successful, so much so that Jack transformed himself and soon assumed the position of President of the X County AA ... a position he now proclaimed at every meeting which he opened with the greeting "Hi, my name is Jack and I'm an alcoholic, ... and the head brewer for XXBB in X County!"
ReplyDelete(This a work of fiction and refers to no persons living or dead. I apologize to all persons and relatives of persons who might think otherwise.)
Fortunately for Jack, brewing and consuming are not the same thing.
ReplyDeleteWhat emptyset was offering, for those brave souls who are still reading, was an example of Russell's Paradox. It presented mathematics with a contradiction that went to the heart of set theory a hundred years ago.
ReplyDeleteActually I use the “Handicap Parking Spot” paradox. Not being able to use a handicap spot is a handicap so I can park in a “handicap spot’, but as soon as I do I no longer have a handicap and have to move.
ReplyDeleteClean. I like that. Of course the moment you decide you have to move ... you no longer have to!
ReplyDeleteI like that too.
ReplyDelete