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WikiCards · Card list · Science cards · Cantor's theorem
Uncommon card · Science
Cantor's theorem, an Uncommon card
In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A, known as the power set of A, has a strictly greater cardinality than A itself.
- Rarity
- Uncommon
- Domain
- Science
- ATK
- 66
- DEF
- 33
- Power
- 99
- Wikipedia reads a year
- 34,000
Power 99 (ATK + DEF): stronger than 55 % of WikiCards cards.
Cantor's theorem quiz: 3 questions
Three questions on the Cantor's theorem card, the way WikiCards duels ask them. Pick an answer, the facts are just below.
Find the missing word
For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of ______.
Answer
subsets. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. From the Cantor's theorem article on Wikipedia.
Which of these cards hits hardest (highest ATK)?
Answer
Cantor's theorem. Cantor's theorem 66 · Microfracture surgery 62 · London sewer system 59 · Clapboard 51 ATK in WikiCards.
In a duel, each round asks a question like these about the opposing card, with 15 seconds to answer.
The facts on the card
The card carries these facts from its Wikipedia article.
- For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets.
- Counting the empty set as a subset, a set with n elements has a total of 2 n subsets, and the theorem holds because 2 n > n for all non-negative integers.
- Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.
Why it is Uncommon
Rarity in WikiCards follows a year of Wikipedia page views: the most read articles become Epic and Legendary cards. The Cantor's theorem article was read about 34,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 66 and blocks with 33: each hit it takes is cut by 13 %.
How to get Cantor's theorem
Open packs. Each pack holds five cards drawn from real Wikipedia articles, the rarest last, and the fifth card is always Rare or better. The odds are shown in the game. A free pack arrives every hour and two can wait, and the Coins you win in duels buy more packs.
More Science cards
Cards close in power
The cards just above and just below Cantor's theorem in the power ranking, all domains together.
- ClapboardUncommon · Science · ATK 51 DEF 48
- Diavik Diamond MineUncommon · Society · ATK 58 DEF 41
- National Service SchemeUncommon · Society · ATK 53 DEF 46
- CriticismUncommon · Arts · ATK 54 DEF 45
- Great Victoria DesertUncommon · Nature · ATK 56 DEF 43
- Hasse diagramUncommon · Science · ATK 57 DEF 42
Card lists
- Wikipedia quizNew questions every day
- All cards from A to ZEvery card, by name
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- Tier listS and A tiers by power (ATK + DEF)
Credits
Text : Wikipedia, Cantor's theorem (revision), CC BY-SA 4.0. Photo : KSmrq, CC BY-SA 3.0, Wikimedia Commons.
