Cantor's theorem

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/cantor-s-theorem

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the discoverer?Georg Cantor (German mathematician)
2. What is the year of publication?1891
3. Why do some infinities seem bigger than others?Because Cantor showed that you can compare infinities, and he proved that the set of all subsets of a set is always a larger infinity than the set itself.
4. How does Cantor's diagonal argument prove the theorem?He imagined a list that pairs every element with a subset, then built a new subset that differs from each listed subset in one element. That new subset can’t be on the list, so the list can’t cover all subsets.

Cardinality: A measure of the 'size' of a set, including infinite sets.
Power Set: The set of all possible subsets of a given set.
Diagonal Argument: A proof technique demonstrating the uncountability of a set by constructing a new element not present in any assumed enumeration.