Cantor's diagonal argument

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/cantors-diagonal-argument

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 proof methodology?Proof by contradiction using diagonalization
2. What is the published year?1891
3. Why does Cantor's argument show that some infinities are bigger than others?The proof shows that if you try to list all real numbers, you can always create a number that is missing from the list. Because you can never finish the list, the real numbers are a bigger infinity than the natural numbers.
4. How does the diagonal argument work with decimal numbers between 0 and 1?Imagine a list of all numbers between 0 and 1 written as infinite decimals. The argument changes each diagonal digit of the list to make a new number that differs from every listed number in at least one place. That new number can’t be on the list, proving the list is incomplete.

Cardinality: A measure of the number of elements in a set, including infinite sets.
Transfinite Numbers: Numbers used to quantify the size of infinite sets, developed by Cantor.
Set Theory: A branch of mathematics concerned with the properties of sets and their operations.