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WikiCards · Card list · Nature cards · Cantor's diagonal argument
Uncommon card · Nature
Cantor's diagonal argument, an Uncommon card
Cantor's diagonal argument is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are sets which in some sense contain more elements than there are positive integers.
- Rarity
- Uncommon
- Domain
- Nature
- ATK
- 69
- DEF
- 54
- Power
- 123
- Wikipedia reads a year
- 100,000
Power 123 (ATK + DEF): stronger than 60 % of WikiCards cards.
Cantor's diagonal argument quiz: 3 questions
Three questions on the Cantor's diagonal argument card, the way WikiCards duels ask them. Pick an answer, the facts are just below.
Find the missing word
Such sets are now called uncountable sets, and the size of ______ sets is treated by the theory of cardinal numbers, which Cantor began.
Answer
infinite. Such sets are now called uncountable sets, and the size of infinite sets is treated by the theory of cardinal numbers, which Cantor began. From the Cantor's diagonal argument article on Wikipedia.
Which of these cards hits hardest (highest ATK)?
Answer
Mathematical proof. Mathematical proof 72 · Cantor's diagonal argument 69 · Great Rift Valley 66 · Aberdeen Angus 62 ATK in WikiCards.
Which of these Wikipedia articles is read the most in a year?
Answer
Great Rift Valley. Great Rift Valley 200,000 · Alstroemeria 130,000 · Cantor's diagonal argument 100,000 · Chlorella 53,000 Wikipedia reads over a year.
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.
- Such sets are now called uncountable sets, and the size of infinite sets is treated by the theory of cardinal numbers, which Cantor began.
- Georg Cantor published this proof in 1891, but it was not his first proof of the uncountability of the real numbers, which appeared in 1874.
- However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the Entscheidungsproblem.
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 diagonal argument article was read about 100,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 69 and blocks with 54: each hit it takes is cut by 22 %.
How to get Cantor's diagonal argument
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.
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The cards just above and just below Cantor's diagonal argument in the power ranking, all domains together.
- Emperor Taizu of SongUncommon · History · ATK 68 DEF 55
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- Aberdeen AngusUncommon · Nature · ATK 62 DEF 61
- Oryza sativaUncommon · Nature · ATK 65 DEF 58
- DidiUncommon · Society · ATK 69 DEF 54
- Mathematical proofUncommon · Science · ATK 72 DEF 51
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Credits
Text : Wikipedia, Cantor's diagonal argument (revision), CC BY-SA 4.0. Photo : Jochen Burghardt, CC BY-SA 3.0, Wikimedia Commons.
