Question

Proving closed interval [0,1] has same cardinality as Real Numbers

score 59 · Answer 1 · 2026-04-15 09:39:59

59

Views

Proving closed interval [0,1] has same cardinality as Real Numbers

Published on 15 Apr 2026 - 9:39

score 432 · Answer 2 · 2026-04-14 20:57:41

432

Views

Are all "Theorems" necessarily in the "if - then" form?

Published on 14 Apr 2026 - 20:57

score 60 · Answer 3 · 2026-04-12 13:51:14

60

Views

How do I show $x^x > k \cdot a^x $?

Published on 12 Apr 2026 - 13:51

score 1.2k · Answer 4 · 2026-04-18 18:24:43

1.2k

Views

Proving the cofinite topology is coarser then the Euclidean topology.

Published on 18 Apr 2026 - 18:24

score 88 · Answer 5 · 2026-04-17 07:39:04

88

Views

Proof by induction of summation inequality: $1 + 1/2+ 1/3+ 1/4+1/5+⋯+ 1/2^n \leq n + 1$

Published on 17 Apr 2026 - 7:39

score 940 · Answer 6 · 2026-04-16 09:53:30

940

Views

Proof that $[a,b)$ is neither closed nor open?

Published on 16 Apr 2026 - 9:53

score 2k · Answer 7 · 2026-04-18 22:32:15

2k

Views

Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$

Published on 18 Apr 2026 - 22:32

score 182 · Answer 8 · 2026-04-14 13:44:37

182

Views

Is Problem Solving In Maths reasoning from previously found results ? Or is there something else I'm missing?

Published on 14 Apr 2026 - 13:44

score 1.7k · Answer 9 · 2026-04-14 23:56:06

1.7k

Views

Saddle point property proof, min max

Published on 14 Apr 2026 - 23:56

score 508 · Answer 10 · 2026-04-14 14:32:25

508

Views

Prove a double inclusion of an arbitrary unions

Published on 14 Apr 2026 - 14:32

score 569 · Answer 11 · 2026-04-11 16:39:18

569

Views

How do I prove that a set $A$ can have at most one least upper bound?

Published on 11 Apr 2026 - 16:39

score 1.5k · Answer 12 · 2026-04-15 05:24:30

1.5k

Views

Suppose a set $A$ is non-empty and bounded above. Given $\epsilon>0$, prove that there is an $a ∈ A$ such that $\sup{A}-\epsilon<a\leq\sup{A}$

Published on 15 Apr 2026 - 5:24

score 114 · Answer 13 · 2026-04-11 07:18:47

114

Views

Equivalence between 2 definitions of closed set.

Published on 11 Apr 2026 - 7:18

score 50 · Answer 14 · 2026-04-16 16:13:53

50

Views

Prove that $|1-x+x^2+x^3| \le \frac{1-|x|^4} {1-|x|}$

Published on 16 Apr 2026 - 16:13

score 150 · Answer 15 · 2026-04-14 04:57:49

150

Views

Consider $A = \{x \in \mathbb{Q} \mid x < \pi \}$. Formally prove that $\sup A = \pi$.

Published on 14 Apr 2026 - 4:57

List Question

Proving closed interval [0,1] has same cardinality as Real Numbers

Are all "Theorems" necessarily in the "if - then" form?

How do I show $x^x > k \cdot a^x $?

Proving the cofinite topology is coarser then the Euclidean topology.

Proof by induction of summation inequality: $1 + 1/2+ 1/3+ 1/4+1/5+⋯+ 1/2^n \leq n + 1$

Proof that $[a,b)$ is neither closed nor open?

Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$

Is Problem Solving In Maths reasoning from previously found results ? Or is there something else I'm missing?

Saddle point property proof, min max

Prove a double inclusion of an arbitrary unions

How do I prove that a set $A$ can have at most one least upper bound?

Suppose a set $A$ is non-empty and bounded above. Given $\epsilon>0$, prove that there is an $a ∈ A$ such that $\sup{A}-\epsilon<a\leq\sup{A}$

Equivalence between 2 definitions of closed set.

Prove that $|1-x+x^2+x^3| \le \frac{1-|x|^4} {1-|x|}$

Consider $A = \{x \in \mathbb{Q} \mid x < \pi \}$. Formally prove that $\sup A = \pi$.

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