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References to 'counterexample'
1. $\Diamond$ by Henry
2. Agoh-Giuga conjecture by PrimeFan
3. arbitrary join by CWoo
4. atom by CWoo
5. Bertrand's conjecture, proof of by CWoo
6. biquadratic field by Wkbj79
7. characterization of a Kleene algebra by CWoo
8. characterization of free submonoids by Ziosilvio
9. Chinese hypothesis by FourDozens
10. combinatorial proof of Zeckendorf's theorem by rm50
11. continuity of composition of functions by bbukh
12. continuous functions on the extended real numbers by Wkbj79
13. continuous nowhere monotonic function by asteroid
14. convergent series where not only$~a_n$ but also $na_n$ tends to 0 by pahio
15. convexity conjecture by PrimeFan
16. decomposable homomorphisms and full families of groups by joking
17. Dilworth's theorem by CWoo
18. Erd\H{o}s-Straus conjecture by CompositeFan
19. Euler's conjecture by PrimeFan
20. every finite dimensional subspace of a normed space is closed by Mathprof
21. example of non-permutable subgroup by Algeboy
22. examples of epis by CWoo
23. examples of monics by CWoo
24. examples supporting the Erd\H{o}s-Straus conjecture by PrimeFan
25. face of a convex set by CWoo
26. false counterexamples to Fermat's last theorem by PrimeFan
27. Feit-Thompson conjecture by PrimeFan
28. Fine and Wilf's theorem on words by Ziosilvio
29. finite nilpotent groups by Algeboy
30. four hundred ninety-six by CompositeFan
31. fourth power by CompositeFan
32. freshman's dream error by Wkbj79
33. graph homeomorphism by Ziosilvio
34. homogeneous polynomial by CWoo
35. ideals contained in a union of ideals by joking
36. Kneser graphs by justice
37. Krystyna Kuperberg by Mravinci
38. large integers that are or might be the smallest of their kind by Mravinci
39. lattice of subgroups by CWoo
40. locally bounded by jirka
41. Marshall Hall's conjecture by PrimeFan
42. mathematics vocabulary by matte
43. meromorphic functions of several variables by jirka
44. Mertens conjecture by PrimeFan
45. normal number by AxelBoldt
46. Peano curve by stevecheng
47. Poincar\'e dodecahedral space by Mathprof
48. Poulet number by CompositeFan
49. probabilistic proof by Algeboy
50. proof by PrimeFan
51. proof of equivalence of Fermat's Last Theorem to its analytic form by whm22
52. proof of uniqueness of center of a circle by CWoo
53. proof that products of connected spaces are connected by yark
54. properties of ordinal arithmetic by CWoo
55. P\'olya's conjecture by PrimeFan
56. Radon measure by ptr
57. Ramanujan prime by PrimeFan
58. Redmond-Sun conjecture by PrimeFan
59. separation axioms by Koro
60. Sloane's conjecture on multiplicative digital root by CompositeFan
61. sums of normal random variables need not be normal by gel
62. Sun Zhiwei by Mravinci
63. table of primes between the first 100 squares by PrimeFan
64. Taylor's formula in Banach spaces by stevecheng
65. the compositum of a Galois extension and another extension is Galois by alozano
66. topological group by yark
67. traveling hump sequence by Wkbj79
68. Tutte theorem by scineram
69. Wall-Sun-Sun prime by PrimeFan