# Discrete Mathematics
Confidence: high
Last verified: 2026-05-22
Generation: human_only


## TL;DR

Discrete mathematics studies countable, distinct (not continuous) structures. It is the mathematical foundation of computer science — covering logic, sets, combinatorics, graph theory, and number theory. Unlike calculus (continuous), discrete math deals with integers, graphs, and logical statements.

## Core Explanation

Combinatorics: counting, permutations (P(n,k) = n!/(n-k)!), combinations (C(n,k) = n!/(k!(n-k)!)). Pigeonhole Principle: if n items in m containers and n > m, at least one container has ≥2 items. Proof techniques: direct, contrapositive, contradiction, induction. Induction: prove base case P(1), then P(k) → P(k+1).

## Further Reading

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