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Induction: the inference of a general law from particular instances. Axiom/ principle: generally acknowledged truth. to prove $∀n$ A$(n)$ Method, principle of mathematical induction Prove A$(1)$ Dominoes: $∀n$ [ A$(n)$ ⇒ A$(n+1)$] induction step Theorem: for any n, 1+2+3 …… + n = 1/2n(n+1) if n = 1, both side equal to 1, then the identity is true. Assume A$(n)$ and deduce A$(n+1)$, the identity holds for all n 1+2+3 …… + n+1 = 1/2(n+1)[(n+1)+1] ...

number theory Number theory | Definition, Topics, & History | Britannica 0 is not a natural number? it depends on the mathematical community, if they design the norm(standard) that 0 i a natural number, then it is. but in a default condition, we normally set 0 is not natural number. b|a Vertical bar sign in Discrete mathematics, means b divides a, b is a factor of a. division theory ? Euclidean division - Wikipedia ...

cognitive conception completeness property 完整属性 upper and lower bound 上界、下界 least upper bound 最小上界 LUB Set theory subset relations Natural numbers, Integers, Rational numbers, Real numbers N ⊂ Z ⊂ Q ⊂ R Elements of Set Theory(SUPPLEMENT, KEITH DEVLIN: Introduction to Mathematical Thinking) empty set ∅ different from Φ(phi) the 21st letter of the Greek alphabet eg. Set A If $A(x)$ is some property, the set of all those x which satisfy $A(x)$ is denoted by {$x | A(x)$} ...

least upper bound A set A of reals can have at most one least upper bound. if a is LUB, then a≤b if b is LUB, then b≤a if a, b are both two LUBs, then b=a, such as {42} has the only element 42 as both an upper bound and a lower bound. lower bound if a set A of reals has a lower bound, it has infinitely many lower bounds. ...

C programming manual 中文：C 语言教程 gnu c library C programming open-source projects suitable for beginners: GeeksforGeeks: This site offers a variety of C projects with source code, categorized by skill level. Some beginner-friendly projects include Rock Paper Scissors, Hangman Game, and Simple Calculator. GitHub Topics: C Projects: Explore various C projects on GitHub. You can find repositories specifically tagged for beginners. Skyfi Labs: This site lists 20 C programming projects for beginners, with source code available on platforms like GitHub. Code with C: A collection of over 50 C/C++ projects with source code, including mini-projects, games, and applications. Practice platform Programiz ...