Number Theory: Operations and Equivalence

Related lectures (29)

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Covers the construction of integers through equivalence relations and their properties in mathematics.

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Covers basic properties of natural numbers, including order relations and inverses.

Covers the basics of group theory, including definitions, examples, and isometries.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Explores division in rational numbers and the extension of addition from integers.

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.