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Math Examples to get High-Schoolers Interested

How did product rule come about historically?

Riddles that can be solved by meta-assumptions

What is the difference between algebraic number theory, arithmetic geometry and diophantine geometry?

Learn Bunch-Kaufman factorization

A grammar question on integrals

Singletons (sets with single element): what's special about them?

Derived sets from a base set

Interaction between pure math and other fields outside of math

Searching for an example of a theorem wich is "easy" to prove in a classical way but way more difficult in the setting of non-standard analysis.

Finding approximate largest common divisor for sets of real numbers.

Which branch of mathematics rigorously defines infinitesimals?

How many elements are there in $\mathbb{Z}_5$?

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Strict infinitesimals and concept of scales.

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