# Mathematics

1. A Rational Number With a Finite Number of Digits
2. Roth vs Traditional, which one is better?
3. Making Sense of Sample Standard Deviation
4. Sample Standard Deviation In Terms of Sum and Square Sum of Samples
5. Proof: Uniqueness of multiplicative inverse
6. Proof: The sum of any three single-digit numbers is at most two digits long
7. Proof: a natural number n is a prime if b^(n−1) = 1 (mod n) for every integer b between 1 and n-1
8. Euler's formula for Planar Graph
9. A number is divisible by 3 iff sum of its digits are divisible by 3
10. 証明:文字列長が素数の文字列集は非正規言語
11. Proof: An Equivalence Relation Defines A Partition
12. Proof: The language consisting of strings whose lengths are prime is not regular
13. Algorithm to Count the Number of On-Bits
14. Numerical Integration Methods
15. Given a rational preference show that indifference relation is also transitive
16. Show that P(A) is a subset of P(B) if A is a subset of B
17. Prove that b | a iff every multiple of a is multiple of b
18. A totally ordered bijective mapping from string to integer
19. A word cannot be described within the same language
20. A complete bipartite graph is a tree only if the order of one of partite sets is 1
21. Fibonacci Numbers in C/C++
22. Prove or disprove if a+b=2 then b+z=3 for some z
23. C(n, r) calculation in C/C++
24. The Second Proof of the Catalan Numbers
25. The Number of R-combinations Repetition Allowed
26. Visualization of the Fundamental Theorem of Calculus

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