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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. Ackermann function is not primitive recursive by CWoo
3. an example of mathematical induction by CWoo
4. an injection between two finite sets of the same cardinality is bijective by alozano
5. another proof of Jensen's inequality by Andrea Ambrosio
6. another proof of pigeonhole principle by ratboy
7. any rational number is a sum of unit fractions by Mathprof
8. cardinality of disjoint union of finite sets by mathcam
9. cardinality of monomials by rspuzio
10. combinations with repeated elements by kfgauss70
11. complete binary tree by akrowne
12. conditional distribution of multi-variate normal variable by stevecheng
13. congruence of arbitrary degree by pahio
14. decomposition of orthogonal operators as rotations and reflections by stevecheng
15. elementary results about multiplicative functions and convolution by Wkbj79
16. Engel's theorem by rmilson
17. equivalent statements of Lindemann-Weierstrass theorem by CWoo
18. every positive integer greater than 30 has at least one composite totative by mps
19. every prime ideal is radical by alozano
20. example of false implies true by Algeboy
21. example of transfinite induction by CWoo
22. extended discussion of the conjugate gradient method by ehremo
23. finitely generated modules over a principal ideal domain by yark
24. formula for sequences satisfying second order recurrence relations by Wkbj79
25. FS iterated forcing preserves chain condition by Henry
26. general commutativity by pahio
27. generalized Schanuel's lemma by CWoo
28. Helly's theorem by bbukh
29. Hofstadter's MIU system by Daume
30. ideals contained in a union of ideals by joking
31. index of set theory by rspuzio
32. induction by Daume
33. intuitionistic logic by gribskoff
34. invariant forms on representations of compact groups by bwebste
35. lemma on projection of countable sets by rspuzio
36. ping-pong lemma by uriw
37. Poincar\'e-Birkhoff-Witt theorem by CWoo
38. prime ideal factorization is unique by gel
39. proof of arithmetic-geometric-harmonic means inequality by drini
40. proof of Bernstein inequalities by Andrea Ambrosio
41. proof of Borsuk-Ulam theorem by bwebste
42. proof of Cassini's identity by yark
43. proof of Chinese remainder theorem by mclase
44. proof of delta system lemma by Henry
45. proof of existence and uniqueness of singular value decomposition by fernsanz
46. proof of finitely generated torsion-free modules over Pr\"ufer domains by gel
47. proof of fundamental theorem of algebra (due to D'Alembert) by rspuzio
48. proof of general associativity by pahio
49. proof of generalized Leibniz rule by rspuzio
50. proof of Gram-Schmidt orthogonalization procedure by rspuzio
51. proof of identity theorem of holomorphic functions by rspuzio
52. proof of Martingale criterion by karstenb
53. proof of pigeonhole principle by Wkbj79
54. proof of Ramsey's theorem by mathcam
55. proof of the Jordan H\"{o}lder decomposition theorem by djao
56. proof of Urysohn's lemma by scanez
57. proof of values of the Riemann zeta function in terms of Bernoulli numbers by rm50
58. proof that $\tau(n)$ is the number of positive divisors of $n$ by Wkbj79
59. properties of Ackermann function by CWoo
60. Ramsey's theorem by bbukh
61. reduction algorithm for symmetric polynomials by djao
62. rigorous definition of tangent function by rspuzio
63. simultaneous block-diagonalization of upper triangular commuting matrices by lars_h
64. simultaneous triangularisation of commuting matrices over any field by lars_h
65. spanning sets of dual space by stevecheng
66. Sylow theorems, proof of by Henry
67. symmetric difference on a finite number of sets by CWoo
68. the inclusion of classical into intuitionistic logic by gribskoff
69. Thom isomorphism theorem by antonio
70. transfinite induction by jihemme
71. uniqueness of cardinality by mathcam
72. upper bound on $\vartheta(n)$ by mps
73. well-ordering principle for natural numbers by smw
74. well-ordering principle for natural numbers proven from the principle of finite induction by smw