What is the cardinality of the set of all people who shall expel us from the paradise that Cantor has created?
October 12, 2012 12:43 PM   Subscribe

Sweet descriptions of the empty set?

In one of the mathematics classes I teach, we have been discussing cardinality (of both infinite and finite sets). So, on the assessment I'm giving them next week, there are some questions just asking "what is the cardinality of [this set]," for various values of [this set].

I want to have all sorts of sets there, including the empty set. But I don't just want to ask them what the cardinality of the empty set is. I'm thinking of "the set of all U.S. presidents born in Mexico" or "the set of months with 40 days" or something.

Do you have any entertaining suggestions for a description I could use?
posted by King Bee to Education (12 answers total) 9 users marked this as a favorite
The set of all people who do no homework in this class, take no quizzes, take no tests, and yet still manage to pass it.
posted by wittgenstein at 12:57 PM on October 12, 2012 [8 favorites]

The set of all days of the week whose names in English don't contain 'y'.
posted by leahwrenn at 1:08 PM on October 12, 2012

The set of female presidents of the United States.

You can match it with {male presidents of the united states} and see how many students are off by 1 because they count Grover Cleveland twice.

(Ok, it's political, not entertaining.)
posted by leahwrenn at 1:10 PM on October 12, 2012 [2 favorites]

The set of words that rhyme with orange.
posted by empath at 1:23 PM on October 12, 2012

The set of all seven letter words in this sentence.
posted by alms at 1:25 PM on October 12, 2012 [9 favorites]

The set of humans who rode on dinosaurs.
posted by milestogo at 1:34 PM on October 12, 2012 [1 favorite]

You could adapt Berkeley's gibe at Newton's infinitesimals, 'the ghosts of departed quantities', and portray it as 'the singular ghost of all departed sets', or 'what's left when you take absolutely everything away.' Though those statements may have their problems-- which could be interesting to discuss perhaps.

It's also the only set for which anything and everything is true of all its elements, and the only set that has a power set with an odd number of elements.

I didn't want to be first to answer this question, because it is a question which is answered if it has no answers.
posted by jamjam at 1:45 PM on October 12, 2012 [7 favorites]

The set of sounds made by one hand clapping. But maybe the answer to that one's not clear.
posted by alms at 4:54 PM on October 12, 2012

Okay, here's one more.

The set of set theories published by Frege that weren't undermined by Bertrand Russell just prior to publication.

But maybe you won't have gotten to that yet.
posted by alms at 5:00 PM on October 12, 2012 [2 favorites]

The set of natural numbers strictly greater than themselves.
The set of natural numbers greater than all other natural numbers.
The set of sets having negative cardinality.
The set of things that cannot be collected into a set.
posted by Jonathan Livengood at 11:24 PM on October 12, 2012

The set of all sets that do not contain the empty set as a subset.
posted by zanni at 12:56 AM on October 13, 2012 [4 favorites]

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