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02-11-2026Challenge 26: Product of a sequence with limit zero and a bounded sequence
25-10-2026Challenge 25: If the interleaving of two sequences converges to L, then both converge to L
19-10-2026Challenge 24: The sequence 1, -1, 1, -1,... is not convergent (2nd version)
12-10-2026Challenge 23: The constant sequence aₙ = L converges to L
10-10-2026Lean 4 for mathematicians: a teacher's guide
05-10-2026Challenge 22: Subsequences with different limits imply non-convergence
28-09-2026Challenge 21: Subsequences have the same limit as the sequence
21-09-2026Challenge 20: If aₙ → L and M is an upper bound of aₙ, then L ≤ M
16-09-2026Challenge 19: Convergent sequences are Cauchy sequences
07-09-2026Challenge 18: Convergence of the product of convergent sequences
30-08-2026Challenge 17: Convergent sequences are bounded
24-08-2026Challenge 16: For every n ∈ N, n(n+1)(2n+1) is divisible by 6
18-08-2026Challenge 15: There exists k ∈ ℕ such that, for all n ∈ ℕ, (n + k)² ≤ 2ⁿ⁺ᵏ
09-08-2026Challenge 14: For all n ∈ ℕ, 2n + 9 ≤ 2ⁿ⁺⁴
03-08-2026Challenge 13: Reverse triangle inequality: ||x| - |y|| ≤ |x - y|
27-07-2026Challenge 12: If aₙ → L, bₙ → M and L < M, then eventually aₙ < bₙ
19-07-2026Challenge 11: If aₙ converges to L, then |aₙ| converges to |L|
13-07-2026Challenge 10: If aₙ → L with L ≠ 0, then |aₙ| ≥ |L|/2 eventually
06-07-2026Challenge 9: Uniqueness of the limit
28-06-2026Challenge 8: Sequences with infinitely many large terms do not converge to small limits
21-06-2026Challenge 7: The composition of injective functions is injective
14-06-2026Challenge 6: If aₙ and cₙ converge to L and aₙ ≤ bₙ ≤ cₙ for all n, then bₙ converges to L
07-06-2026Challenge 5: 5²ⁿ - 2³ⁿ is divisible by 17
03-06-2026If a converges to L, then (∃ N)(∀ n ≥ N)[aₙ ≥ L - 1]
01-06-2026If aₙ converges to L and bₙ to M, then aₙ+bₙ converges to L+M.
31-05-2026Challenge 4: There are infinitely many prime numbers
24-05-2026Challenge 3: If aₙ converges to L, then 2aₙ converges to 2L
17-05-2026Challenge 2: The sequence 1, -1, 1, -1,... is not convergent
10-05-2026Challenge 1: The sequence 1/n converges to 0
09-05-2026Proof challenges in Lean 4
21-01-2025Praeclarum theorema
03-01-2025Nicomachus’s theorem
02-12-2024If uₙ tends to a y vₙ tends to b, then uₙvₙ tends to ab
29-11-2024If the limit of the sequence u(n) is a and c ∈ ℝ, then the limit of u(n)c is ac
10-11-2024If u(n) tends to a, then 7u(n) tends to 7a
07-10-2024Pigeonhole principle
04-10-2024If f ∘ f is bijective, then f is bijective
25-09-2024Brahmagupta-Fibonacci identity
24-09-2024Proofs of ∑k<n. 2ᵏ = 2ⁿ-1
19-09-2024Proofs of "∑i<n. i = n(n-1)/2"
12-09-2024Proofs of "If p > -1, then (1+p)ⁿ ≥ 1+np"
10-09-2024Proofs of 0³+1³+2³+3³+···+n³ = (n(n+1)/2)²
09-09-2024Proofs of a+aq+aq²+···+aqⁿ = a(1-qⁿ⁺¹)/(1-q)
07-09-2024Proofs of a+(a+d)+(a+2d)+···+(a+nd)=(n+1)(2a+nd)/2
05-09-2024Proofs of "0+1+2+3+···+n=n(n + 1)/2"
04-09-2024If f is continuous at a and the limit of u(n) is a, then the limit of f(u(n)) is f(a)
03-09-2024If x is the limit of u and y is an upper bound of u, then x ≤ y
02-09-2024If (∀ ε > 0, y ≤ x + ε), then y ≤ x
31-08-2024If x is the supremum of set A, then ((∀ y)[y < x → (∃ a ∈ A)[y < a]]
29-08-2024Equivalence of definitions of the Fibonacci function
28-08-2024Proofs of "flatten (mirror a) = reverse (flatten a)"
26-08-2024Proofs that the mirror function of binary trees is involutive
19-08-2024Equivalence of reverse definitions
14-08-2024Proofs of take n xs ++ drop n xs = xs
07-08-2024Proofs of the equality length(xs ++ ys) = length(xs) + length(ys)