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References to 'principle of finite induction'
1. a polynomial of degree $n$ over a field has at most $n$ roots by alozano
2. an example of mathematical induction by CWoo
3. an injection between two finite sets of the same cardinality is bijective by alozano
4. another proof of Jensen's inequality by Andrea Ambrosio
5. another proof of pigeonhole principle by ratboy
6. any rational number is a sum of unit fractions by Mathprof
7. cardinality of disjoint union of finite sets by mathcam
8. cardinality of monomials by rspuzio
9. combinations with repeated elements by kfgauss70
10. complete binary tree by akrowne
11. conditional distribution of multi-variate normal variable by stevecheng
12. congruence of arbitrary degree by pahio
13. decomposition of orthogonal operators as rotations and reflections by stevecheng
14. elementary results about multiplicative functions and convolution by Wkbj79
15. Engel's theorem by rmilson
16. equivalent statements of Lindemann-Weierstrass theorem by CWoo
17. every positive integer greater than 30 has at least one composite totative by mps
18. every prime ideal is radical by alozano
19. example of false implies true by Algeboy
20. example of transfinite induction by CWoo
21. extended discussion of the conjugate gradient method by ehremo
22. finitely generated modules over a principal ideal domain by yark
23. formula for sequences satisfying second order recurrence relations by Wkbj79
24. FS iterated forcing preserves chain condition by Henry
25. general commutativity by pahio
26. generalized Schanuel's lemma by CWoo
27. Helly's theorem by bbukh
28. Hofstadter's MIU system by Daume
29. ideals contained in a union of ideals by joking
30. index of set theory by rspuzio
31. induction by Daume
32. intuitionistic logic by gribskoff
33. invariant forms on representations of compact groups by bwebste
34. lemma on projection of countable sets by rspuzio
35. ping-pong lemma by uriw
36. Poincar\'e-Birkhoff-Witt theorem by CWoo
37. prime ideal factorization is unique by gel
38. proof of arithmetic-geometric-harmonic means inequality by drini
39. proof of Bernstein inequalities by Andrea Ambrosio
40. proof of Borsuk-Ulam theorem by bwebste
41. proof of Cassini's identity by yark
42. proof of Chinese remainder theorem by mclase
43. proof of delta system lemma by Henry
44. proof of existence and uniqueness of singular value decomposition by fernsanz
45. proof of finitely generated torsion-free modules over Pr\"ufer domains by gel
46. proof of fundamental theorem of algebra (due to D'Alembert) by rspuzio
47. proof of general associativity by pahio
48. proof of generalized Leibniz rule by rspuzio
49. proof of Gram-Schmidt orthogonalization procedure by rspuzio
50. proof of identity theorem of holomorphic functions by rspuzio
51. proof of Martingale criterion by karstenb
52. proof of pigeonhole principle by Wkbj79
53. proof of Ramsey's theorem by mathcam
54. proof of the Jordan H\"{o}lder decomposition theorem by djao
55. proof of Urysohn's lemma by scanez
56. proof of values of the Riemann zeta function in terms of Bernoulli numbers by rm50
57. proof that $\tau(n)$ is the number of positive divisors of $n$ by Wkbj79
58. Ramsey's theorem by bbukh
59. reduction algorithm for symmetric polynomials by djao
60. rigorous definition of tangent function by rspuzio
61. simultaneous block-diagonalization of upper triangular commuting matrices by lars_h
62. simultaneous triangularisation of commuting matrices over any field by lars_h
63. spanning sets of dual space by stevecheng
64. Sylow theorems, proof of by Henry
65. symmetric difference on a finite number of sets by CWoo
66. the inclusion of classical into intuitionistic logic by gribskoff
67. Thom isomorphism theorem by antonio
68. transfinite induction by jihemme
69. uniqueness of cardinality by mathcam
70. upper bound on $\vartheta(n)$ by mps
71. well-ordering principle for natural numbers by smw
72. well-ordering principle for natural numbers proven from the principle of finite induction by smw