Question

Define a relation R on R by xRy if and only if y − x ∈ Z.

score 3.5k · Answer 1 · 2026-04-15 00:58:09

3.5k

Views

Define a relation R on R by xRy if and only if y − x ∈ Z.

Published on 15 Apr 2026 - 0:58

score 43 · Answer 2 · 2026-04-16 02:10:01

43

Views

How can I prove (or state that this statement is wrong) "For any real number $x$, if $x < x$ then $x$ is a rational number."

Published on 16 Apr 2026 - 2:10

score 32 · Answer 3 · 2026-04-12 11:32:09

32

Views

How to prove fundamental lemma of homogeneous linear equations using induction.

Published on 12 Apr 2026 - 11:32

score 314 · Answer 4 · 2026-04-17 10:25:21

314

Views

Expression $\lambda e^{-\lambda} \sum_{k \ge 1} \frac{1}{(k - 1)!} \lambda^{k - 1}$ in expectation of Poisson distribution proof

Published on 17 Apr 2026 - 10:25

score 1k · Answer 5 · 2026-04-16 16:01:54

1k

Views

Between two Real Numbers exists Rational Number

Published on 16 Apr 2026 - 16:01

score 131 · Answer 6 · 2026-03-28 07:15:48

131

Views

Prove that $a^{2} \sqrt{b^{2}-b c+c^{2}}+b^{2} \sqrt{c^{2}-c a+a^{2}}+c^{2} \sqrt{a^{2}-a b+b^{2}} \leq a^{3}+b^{3}+c^{3}$

Published on 28 Mar 2026 - 7:15

score 753 · Answer 7 · 2026-04-13 05:34:43

753

Views

Show that a uniformly continuous function on $E$ has a unique continuous extension to $cl(E)$

Published on 13 Apr 2026 - 5:34

score 126 · Answer 8 · 2026-04-14 17:22:47

126

Views

Prove f(x) =0 for all x belonging to [0,1]

Published on 14 Apr 2026 - 17:22

score 118 · Answer 9 · 2026-04-16 08:30:32

118

Views

Prove $|f(y)−f(x)−f′(x)(y−x)|≤ε|y−x|, ∀x,y∈[0,1], |x−y|<δ$.

Published on 16 Apr 2026 - 8:30

score 83 · Answer 10 · 2026-04-14 04:51:18

83

Views

What assumptions can be made in the proof by contradiction of $\sqrt{2}$ is irrational.

Published on 14 Apr 2026 - 4:51

score 51 · Answer 11 · 2026-04-08 18:46:31

51

Views

Let $u$ be transcendental over $\mathbb{Z}_p$. Why is $t^p-u$ irreducible over $\mathbb{Z}_p(u)$?

Published on 08 Apr 2026 - 18:46

score 480 · Answer 12 · 2026-04-30 06:10:38

480

Views

Rudin: Cauchy-Schwarz inequality

Published on 30 Apr 2026 - 6:10

score 175 · Answer 13 · 2026-04-15 22:43:24

175

Views

Clustering number on ring lattice

Published on 15 Apr 2026 - 22:43

score 277 · Answer 14 · 2026-04-14 00:10:28

277

Views

why compact operator has countable number of eigenvalues?

Published on 14 Apr 2026 - 0:10

score 85 · Answer 15 · 2026-04-14 15:00:06

85

Views

Help with a proof that $\lim_{x \to 0} \frac{a^x-1}{x}$ exists

Published on 14 Apr 2026 - 15:00

List Question

Define a relation R on R by xRy if and only if y − x ∈ Z.

How can I prove (or state that this statement is wrong) "For any real number $x$, if $x < x$ then $x$ is a rational number."

How to prove fundamental lemma of homogeneous linear equations using induction.

Expression $\lambda e^{-\lambda} \sum_{k \ge 1} \frac{1}{(k - 1)!} \lambda^{k - 1}$ in expectation of Poisson distribution proof

Between two Real Numbers exists Rational Number

Prove that $a^{2} \sqrt{b^{2}-b c+c^{2}}+b^{2} \sqrt{c^{2}-c a+a^{2}}+c^{2} \sqrt{a^{2}-a b+b^{2}} \leq a^{3}+b^{3}+c^{3}$

Show that a uniformly continuous function on $E$ has a unique continuous extension to $cl(E)$

Prove f(x) =0 for all x belonging to [0,1]

Prove $|f(y)−f(x)−f′(x)(y−x)|≤ε|y−x|, ∀x,y∈[0,1], |x−y|<δ$.

What assumptions can be made in the proof by contradiction of $\sqrt{2}$ is irrational.

Let $u$ be transcendental over $\mathbb{Z}_p$. Why is $t^p-u$ irreducible over $\mathbb{Z}_p(u)$?

Rudin: Cauchy-Schwarz inequality

Clustering number on ring lattice

why compact operator has countable number of eigenvalues?

Help with a proof that $\lim_{x \to 0} \frac{a^x-1}{x}$ exists

Trending Questions

Popular # Hahtags

Popular Questions